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18.175 Theory of Probability (MIT) 18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory. This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.Subjects

Earth | Earth | Solar System | Solar System | Geophysics | Geophysics | Gravitational Field | Gravitational Field | Magnetic Field | Magnetic Field | Seismology | Seismology | Geodynamics | Geodynamics | Laws of large numbers | Laws of large numbers | central limit theorems for sums of independent random variables | central limit theorems for sums of independent random variables | conditioning and martingales | conditioning and martingales | Brownian motion and elements of diffusion theory | Brownian motion and elements of diffusion theory | functional limit theorems | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT) 18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory. This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.Subjects

Earth | Earth | Solar System | Solar System | Geophysics | Geophysics | Gravitational Field | Gravitational Field | Magnetic Field | Magnetic Field | Seismology | Seismology | Geodynamics | Geodynamics | Laws of large numbers | Laws of large numbers | central limit theorems for sums of independent random variables | central limit theorems for sums of independent random variables | conditioning and martingales | conditioning and martingales | Brownian motion and elements of diffusion theory | Brownian motion and elements of diffusion theory | functional limit theorems | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT) 18.175 Theory of Probability (MIT)

Description

This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales. This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.Subjects

Laws of large numbers | Laws of large numbers | central limit theorems | central limit theorems | independent random variables | independent random variables | conditioning | conditioning | martingales | martingales | Brownian motion | Brownian motion | elements of diffusion theory | elements of diffusion theory | functional limit theorems | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT) 18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory. This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.Subjects

Earth | Earth | Solar System | Solar System | Geophysics | Geophysics | Gravitational Field | Gravitational Field | Magnetic Field | Magnetic Field | Seismology | Seismology | Geodynamics | Geodynamics | Laws of large numbers | Laws of large numbers | central limit theorems for sums of independent random variables | central limit theorems for sums of independent random variables | conditioning and martingales | conditioning and martingales | Brownian motion and elements of diffusion theory | Brownian motion and elements of diffusion theory | functional limit theorems | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | central limit theorems | continuous-time random walks | continuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation | percolation | percolationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.Subjects

Discrete and continuum modeling of diffusion processes in physics | Discrete and continuum modeling of diffusion processes in physics | chemistry | chemistry | and economics | and economics | central limit theorems | central limit theorems | ontinuous-time random walks | ontinuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.436J Fundamentals of Probability (MIT) 6.436J Fundamentals of Probability (MIT)

Description

This is a course on the fundamentals of probability geared towards first- or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in 6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations. This is a course on the fundamentals of probability geared towards first- or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in 6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations.Subjects

sample space | sample space | random variables | random variables | expectations | expectations | transforms | transforms | Bernoulli process | Bernoulli process | Poisson process | Poisson process | Markov chains | Markov chains | limit theorems | limit theorems | measure theory | measure theoryLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.100A Introduction to Analysis (MIT) 18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plaSubjects

mathematical analysis | mathematical analysis | estimations | estimations | limit of a sequence | limit of a sequence | limit theorems | limit theorems | subsequences | subsequences | cluster points | cluster points | infinite series | infinite series | power series | power series | local and global properties | local and global properties | continuity | continuity | intermediate-value theorem | intermediate-value theorem | convexity | convexity | integrability | integrability | Riemann integral | Riemann integral | calculus | calculus | convergence | convergence | Gamma function | Gamma function | Stirling | Stirling | quantifiers and negation | quantifiers and negation | Leibniz | Leibniz | Fubini | Fubini | improper integrals | improper integrals | Lebesgue integral | Lebesgue integral | mathematical proofs | mathematical proofs | differentiation | differentiation | integration | integrationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.Subjects

Earth | Solar System | Geophysics | Gravitational Field | Magnetic Field | Seismology | Geodynamics | Laws of large numbers | central limit theorems for sums of independent random variables | conditioning and martingales | Brownian motion and elements of diffusion theory | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | central limit theorems | continuous-time random walks | continuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation | percolation | percolationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.070J Advanced Stochastic Processes (MIT) 15.070J Advanced Stochastic Processes (MIT)

Description

This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models. This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.Subjects

analysis | analysis | modeling | modeling | stochastic processes | stochastic processes | theoretic probability | theoretic probability | martingales | martingales | filtration | filtration | stopping theorems | stopping theorems | large deviations theory | large deviations theory | Brownian motion | Brownian motion | reflected Brownian motion | reflected Brownian motion | stochastic integration | stochastic integration | Ito calculus | Ito calculus | functional limit theorems | functional limit theorems | applications | applications | finance theory | finance theory | insurance | insurance | queueing | queueing | inventory models | inventory modelsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.070 Advanced Stochastic Processes (MIT) 15.070 Advanced Stochastic Processes (MIT)

Description

The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models. The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.Subjects

analysis | analysis | modeling | modeling | stochastic processes | stochastic processes | theoretic probability | theoretic probability | martingales | martingales | filtration | filtration | stopping theorems | stopping theorems | large deviations theory | large deviations theory | Brownian motion | Brownian motion | reflected Brownian motion | reflected Brownian motion | stochastic integration | stochastic integration | Ito calculus | Ito calculus | functional limit theorems | functional limit theorems | applications | applications | finance theory | finance theory | insurance | insurance | queueing | queueing | inventory models | inventory modelsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.Subjects

Earth | Solar System | Geophysics | Gravitational Field | Magnetic Field | Seismology | Geodynamics | Laws of large numbers | central limit theorems for sums of independent random variables | conditioning and martingales | Brownian motion and elements of diffusion theory | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.Subjects

Earth | Solar System | Geophysics | Gravitational Field | Magnetic Field | Seismology | Geodynamics | Laws of large numbers | central limit theorems for sums of independent random variables | conditioning and martingales | Brownian motion and elements of diffusion theory | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.Subjects

Earth | Solar System | Geophysics | Gravitational Field | Magnetic Field | Seismology | Geodynamics | Laws of large numbers | central limit theorems for sums of independent random variables | conditioning and martingales | Brownian motion and elements of diffusion theory | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.175 Theory of Probability (MIT)

Description

This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.Subjects

Laws of large numbers | central limit theorems | independent random variables | conditioning | martingales | Brownian motion | elements of diffusion theory | functional limit theoremsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.070 Advanced Stochastic Processes (MIT)

Description

The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.Subjects

analysis | modeling | stochastic processes | theoretic probability | martingales | filtration | stopping theorems | large deviations theory | Brownian motion | reflected Brownian motion | stochastic integration | Ito calculus | functional limit theorems | applications | finance theory | insurance | queueing | inventory modelsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.070 Advanced Stochastic Processes (MIT)

Description

The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.Subjects

analysis | modeling | stochastic processes | theoretic probability | martingales | filtration | stopping theorems | large deviations theory | Brownian motion | reflected Brownian motion | stochastic integration | Ito calculus | functional limit theorems | applications | finance theory | insurance | queueing | inventory modelsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | continuous-time random walks | Levy flights | correlations | extreme events | mixing | renormalization | and percolation | percolationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.366 Random Walks and Diffusion (MIT)

Description

Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | ontinuous-time random walks | Levy flights | correlations | extreme events | mixing | renormalization | and percolationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.070J Advanced Stochastic Processes (MIT)

Description

This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.Subjects

analysis | modeling | stochastic processes | theoretic probability | martingales | filtration | stopping theorems | large deviations theory | Brownian motion | reflected Brownian motion | stochastic integration | Ito calculus | functional limit theorems | applications | finance theory | insurance | queueing | inventory modelsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plaSubjects

mathematical analysis | estimations | limit of a sequence | limit theorems | subsequences | cluster points | infinite series | power series | local and global properties | continuity | intermediate-value theorem | convexity | integrability | Riemann integral | calculus | convergence | Gamma function | Stirling | quantifiers and negation | Leibniz | Fubini | improper integrals | Lebesgue integral | mathematical proofs | differentiation | integrationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | continuous-time random walks | Levy flights | correlations | extreme events | mixing | renormalization | and percolation | percolationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.436J Fundamentals of Probability (MIT)

Description

This is a course on the fundamentals of probability geared towards first- or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in 6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations.Subjects

sample space | random variables | expectations | transforms | Bernoulli process | Poisson process | Markov chains | limit theorems | measure theoryLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata