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6.262 Discrete Stochastic Processes (MIT) 6.262 Discrete Stochastic Processes (MIT)

Description

Includes audio/video content: AV lectures. Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance. Includes audio/video content: AV lectures. Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.

Subjects

probability | probability | Poisson processes | Poisson processes | finite-state Markov chains | finite-state Markov chains | renewal processes | renewal processes | countable-state Markov chains | countable-state Markov chains | Markov processes | Markov processes | countable state spaces | countable state spaces | random walks | random walks | large deviations | large deviations | martingales | martingales

License

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.htm

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15.070J 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 models

License

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.htm

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15.070 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 models

License

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.htm

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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.

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 models

License

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.htm

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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.

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 models

License

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.htm

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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.

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 models

License

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.htm

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https://ocw.mit.edu/rss/all/mit-allcourses.xml

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6.262 Discrete Stochastic Processes (MIT)

Description

Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.

Subjects

probability | Poisson processes | finite-state Markov chains | renewal processes | countable-state Markov chains | Markov processes | countable state spaces | random walks | large deviations | martingales

License

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.htm

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https://ocw.mit.edu/rss/all/mit-allcourses.xml

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