Stochastic processes and applications DSBA 2025/2026 — различия между версиями
Bdemeshev (обсуждение | вклад) |
Agpopov (обсуждение | вклад) |
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| (не показаны 3 промежуточные версии этого же участника) | |||
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Hand made [https://e.pcloud.link/publink/show?code=kZj5BOZAb8qNTSGI6LiGLeLWvMd4LMu4hsk videos with love]! | Hand made [https://e.pcloud.link/publink/show?code=kZj5BOZAb8qNTSGI6LiGLeLWvMd4LMu4hsk videos with love]! | ||
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| + | Class notes [https://disk.360.yandex.ru/d/ViBiodE8BPk2Aw disk] | ||
=== Home assignments, exams and grading === | === Home assignments, exams and grading === | ||
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2025-09-02, lecture 1: Rules of the game, definition of a Markov chain, Chapman-Kolmogorov equations, calculation of n-step transition probabilities, failed attempt to discuss first step analysis. Check 1.1-2.1 from [https://www.statslab.cam.ac.uk/~rrw1/markov/M.pdf Mchains] | 2025-09-02, lecture 1: Rules of the game, definition of a Markov chain, Chapman-Kolmogorov equations, calculation of n-step transition probabilities, failed attempt to discuss first step analysis. Check 1.1-2.1 from [https://www.statslab.cam.ac.uk/~rrw1/markov/M.pdf Mchains] | ||
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| + | 2025-09-30, lecture 5: Irreducible chain. Proportion of life spent at a node wo proof. Knight on the chessboard problem. Stationary state. Period of a node. Aperiodic node. Existence of a stationary distribution wo proof. Convergence to a stationary distribution wo proof. | ||
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| + | 2025-10-07, lecture 6: Convergence in probability. Convergence almost surely. Convergence in mean. Convergence in distribution. Examples. Relationship between convergence modes wo proof. | ||
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| + | 2025-11-11, lecture 9: Три определения пуассоновского потока и (на 75%) доказательство их эквивалентности. Через экспоненциальное, через Пуассона и через о-малые. Формулировку свойств минимума экспоненциальных распределений без доказательств. Определение марковской цепи в непрерывном времени (через экспоненциальные времена в каждом состоянии). | ||
Текущая версия на 11:47, 15 ноября 2025
Содержание
Course goals
侍には目標がなく道しかない [Samurai niwa mokuhyō ga naku michi shikanai]
A samurai has no goal, only a path.
Course whitepaper
Telegram chat (не берёт на парковке)
Hand made videos with love!
Class notes disk
Home assignments, exams and grading
Stochastic Processes = 0.35 Halloween Exam + 0.40 Ded Moroz Exam + 0.25 Home Assignments
Almost surely every week a new home assignment will be published. You are not required to hand in the HA, but next class will include a quiz with one or two problems extremely similar to the HA. Once during the course HA will be in the form of a computer assisted project. At the end of the course you have 5 honey pots: a right to rewrite 5 missed or badly written quizzes.
Samurai diary: Stochastic Process
2025-09-02, lecture 1: Rules of the game, definition of a Markov chain, Chapman-Kolmogorov equations, calculation of n-step transition probabilities, failed attempt to discuss first step analysis. Check 1.1-2.1 from Mchains
2025-09-30, lecture 5: Irreducible chain. Proportion of life spent at a node wo proof. Knight on the chessboard problem. Stationary state. Period of a node. Aperiodic node. Existence of a stationary distribution wo proof. Convergence to a stationary distribution wo proof.
2025-10-07, lecture 6: Convergence in probability. Convergence almost surely. Convergence in mean. Convergence in distribution. Examples. Relationship between convergence modes wo proof.
2025-11-11, lecture 9: Три определения пуассоновского потока и (на 75%) доказательство их эквивалентности. Через экспоненциальное, через Пуассона и через о-малые. Формулировку свойств минимума экспоненциальных распределений без доказательств. Определение марковской цепи в непрерывном времени (через экспоненциальные времена в каждом состоянии).
Classes
2025-09-06, class 1:
Sources of Wisdom
StoPro: Problems in Stochastic Processes
In2Pro: Blitstein, Hwang, Introduction to probability.
Mchains Cambridge lectures on Markov chains.
MarkovTex: Representing Markov Chains in Latex.
Takis: Takis Konstantinopulos, One hundred solved exercises on Markov chains.
Convergence modes review from Cornell university
Convergence modes: Saravan Vijayakumaran, convergence modes with examples
ts2010: Aad van der Vaart, Time Series course with hardcore math
Past course iterations: 2024-2025, 2023-2024, 2022-2023, 2021-2022, 2020-2021.
