Tssp-2024-25 — различия между версиями
Bdemeshev (обсуждение | вклад) |
Bdemeshev (обсуждение | вклад) |
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| (не показано 17 промежуточных версии этого же участника) | |||
| Строка 26: | Строка 26: | ||
[https://github.com/bdemeshev/tssp_exams/raw/main/tssp_exams.pdf Past exams] | [https://github.com/bdemeshev/tssp_exams/raw/main/tssp_exams.pdf Past exams] | ||
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| + | '''Midterm alpha: Tuesday, 5 November at 18:10.''' | ||
== Samurai diary == | == Samurai diary == | ||
| Строка 31: | Строка 33: | ||
Lecture slides and class [https://github.com/bdemeshev/hse_panda_tssp_2024_2025/tree/main/course_notes notes] | Lecture slides and class [https://github.com/bdemeshev/hse_panda_tssp_2024_2025/tree/main/course_notes notes] | ||
| − | 2024-09- | + | 2024-09-02, lecture 1: |
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| + | 2024-09-09, lecture 2: | ||
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| + | 2024-09-16, lecture 3: Markov chain: communicating classes. Transient states. Recurrent states. | ||
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| + | 2024-09-24, lecture 4: Idea of generating function: describe collection of objects as a function and extract information from function. | ||
| + | How to extract E(X), E(X^2), E(XY), P(X=3) from a function that generates outcomes. Formal definition of probability generating function and moment generating function. | ||
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| + | 2024-10-30, lecture 5: | ||
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| + | 2024-10-07, lecture 6: | ||
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| + | 2024-10-14, lecture 7: Sigma-algebra is a way to model information, formal definition. Calculating sigma-algebra generated by two events or by discrete random variable. | ||
| + | Filtration is a growing sequence of sigma-algebras. Formal definition of conditional expected value with respect to sigma-algebra. | ||
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| + | 2024-10-21, lecture 8: | ||
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| + | 2024-12-02, lecture: Girsanov theorem, European option pricing in the Black and Scholes model | ||
| Строка 38: | Строка 59: | ||
Class [https://e.pcloud.link/publink/show?code=kZDCKPZ6dPB3lXGHrhUzqeC7wkVfyaLsAq7 video recordings] | Class [https://e.pcloud.link/publink/show?code=kZDCKPZ6dPB3lXGHrhUzqeC7wkVfyaLsAq7 video recordings] | ||
| − | 2024-09-06: First step analysis, | + | Maria Kirillova [https://disk.yandex.ru/d/5gs97BDSjwmOSw notes] |
| + | |||
| + | 2024-09-06, class 1: First step analysis, 1.1 from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro]. | ||
More on first step analysis: section 2.7.2 in [https://projects.iq.harvard.edu/stat110/home In2Pro] | More on first step analysis: section 2.7.2 in [https://projects.iq.harvard.edu/stat110/home In2Pro] | ||
| − | 2024-09-13: First step analysis, | + | 2024-09-13, class 2: First step analysis, 1.4 from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro]. |
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| + | 2024-09-20, class 3: Classification of states in Markov chain, communicating classes, 3.1ab from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro]. | ||
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| + | 2024-09-27, class 4: Generating functions: standard normal distribution, chi-squared with 1 degree of freedom. | ||
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| + | 2024-10-04, class 5: Calculating probability limit using LLN. Intuition behind probability limit: unique forecast that is "arbitrary good" for almost all X_n. | ||
| + | Probability limit of max and min. Probability limit is a random variable. Probability limit of iid sequence does not exist. | ||
| + | |||
| + | 2024-10-11, class 6: Two more limits (in probability and in L2), conditional expected value in uniform case, conditional expected value with joint density. | ||
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| + | 2024-10-18, class 7: Calculation of sigma-algebra generated by random variable. Calculation of expected value wrt to sigma-algebra. | ||
| + | |||
| + | 2024-11-01, class 8: Checking that a process is a martingale, 9.1abcd, 9.9 from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro]. | ||
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| + | 2024-11-08, class 9: Poisson point process | ||
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| + | 2024-11-15, class 10: Doob's optional stopping time theorem in discrete time | ||
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| + | 2024-11-22, class 11: Calculating E, Cov, Var for Wiener process, (W_t) and (W_t^2 - t) are martingales | ||
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| + | 2024-11-29, class 12: Ito's integral for a piece-wise constant process, Ito's lemma, martingale condition | ||
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| + | 2024-12-06, class 13: more Ito's lemma and stochastic integral properties. | ||
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| + | 2024-12-13, class 14: binomial tree, finding risk neutral probabilities, European and American call option. | ||
== Sources of Wisdom == | == Sources of Wisdom == | ||
| Строка 55: | Строка 103: | ||
[https://www.stat.berkeley.edu/~aldous/150/takis_exercises.pdf Takis]: Takis Konstantinopulos, One hundred solved exercises on Markov chains. | [https://www.stat.berkeley.edu/~aldous/150/takis_exercises.pdf Takis]: Takis Konstantinopulos, One hundred solved exercises on Markov chains. | ||
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| + | Past course iterations: [http://wiki.cs.hse.ru/Tssp-2023-24 2023-2024], [http://wiki.cs.hse.ru/Tssp-2022-23 2022-2023], [http://wiki.cs.hse.ru/Time_Series_and_Stochastic_Processes_ada_21_22 2021-2022], [http://wiki.cs.hse.ru/Time_Series_and_Stochastic_Processes_ada_20_21 2020-2021]. | ||
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| + | [https://courses.cit.cornell.edu/econ620/reviewm6.pdf Convergence modes] review from Cornell university | ||
| + | |||
| + | [https://www.ee.iitb.ac.in/~sarva/courses/EE325/2014/Slides/ConvergenceOfRVs.pdf Convergence modes]: Saravan Vijayakumaran, convergence modes with examples | ||
Текущая версия на 15:49, 15 декабря 2024
Содержание
What-about
Course whitepaper
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.
Telegram chat
Grading
Stochastic Processes = 0.35 Halloween Exam + 0.40 Ded Moroz Exam + 0.25 Home Assignments
Time Series Analysis = 0.30 Mimoza Exam + 0.45 Sakura Exam + 0.25 Home Assignments
Home assignments
Home assignments have equal weights. You have 4 honey weeks for the whole year.
Exams
Midterm alpha: Tuesday, 5 November at 18:10.
Samurai diary
Lecture slides and class notes
2024-09-02, lecture 1:
2024-09-09, lecture 2:
2024-09-16, lecture 3: Markov chain: communicating classes. Transient states. Recurrent states.
2024-09-24, lecture 4: Idea of generating function: describe collection of objects as a function and extract information from function. How to extract E(X), E(X^2), E(XY), P(X=3) from a function that generates outcomes. Formal definition of probability generating function and moment generating function.
2024-10-30, lecture 5:
2024-10-07, lecture 6:
2024-10-14, lecture 7: Sigma-algebra is a way to model information, formal definition. Calculating sigma-algebra generated by two events or by discrete random variable. Filtration is a growing sequence of sigma-algebras. Formal definition of conditional expected value with respect to sigma-algebra.
2024-10-21, lecture 8:
2024-12-02, lecture: Girsanov theorem, European option pricing in the Black and Scholes model
Classes
Class video recordings
Maria Kirillova notes
2024-09-06, class 1: First step analysis, 1.1 from StoPro.
More on first step analysis: section 2.7.2 in In2Pro
2024-09-13, class 2: First step analysis, 1.4 from StoPro.
2024-09-20, class 3: Classification of states in Markov chain, communicating classes, 3.1ab from StoPro.
2024-09-27, class 4: Generating functions: standard normal distribution, chi-squared with 1 degree of freedom.
2024-10-04, class 5: Calculating probability limit using LLN. Intuition behind probability limit: unique forecast that is "arbitrary good" for almost all X_n. Probability limit of max and min. Probability limit is a random variable. Probability limit of iid sequence does not exist.
2024-10-11, class 6: Two more limits (in probability and in L2), conditional expected value in uniform case, conditional expected value with joint density.
2024-10-18, class 7: Calculation of sigma-algebra generated by random variable. Calculation of expected value wrt to sigma-algebra.
2024-11-01, class 8: Checking that a process is a martingale, 9.1abcd, 9.9 from StoPro.
2024-11-08, class 9: Poisson point process
2024-11-15, class 10: Doob's optional stopping time theorem in discrete time
2024-11-22, class 11: Calculating E, Cov, Var for Wiener process, (W_t) and (W_t^2 - t) are martingales
2024-11-29, class 12: Ito's integral for a piece-wise constant process, Ito's lemma, martingale condition
2024-12-06, class 13: more Ito's lemma and stochastic integral properties.
2024-12-13, class 14: binomial tree, finding risk neutral probabilities, European and American call option.
Sources of Wisdom
StoPro: Problems in Stochastic Processes
In2Pro: Blitstein, Hwang, Introduction to probability.
MarkovTex: Representing Markov Chains in Latex.
Mchains Cambridge lectures on Markov chains.
Takis: Takis Konstantinopulos, One hundred solved exercises on Markov chains.
Past course iterations: 2023-2024, 2022-2023, 2021-2022, 2020-2021.
Convergence modes review from Cornell university
Convergence modes: Saravan Vijayakumaran, convergence modes with examples
