Stochastic analysis 2020 2021 — различия между версиями

Версия 11:10, 6 сентября 2020

Lecturers and Seminarists

About the course

This page contains materials for Stochastic Analysis course in 2020/2021 year, mandatory one for 1st year master students of Statistical Learning Theory program (HSE and Skoltech).

Grading formula

The final grade consists of 4 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :

• O_HW for the hometasks
• O_Mid-term for the midterm exam
• O_Exam for the final exam

The formula for the final grade is

• O_Final = 0.3*O_HW + 0.3*O_Mid-term + 0.4*O_Exam

with the usual (arithmetical) rounding rule.

Lectures

• Lecture 05.09

Seminars

• To be filled

Midterm

Grades and results

• Results

Recommended literature (1st term)

• http://www.statslab.cam.ac.uk/~james/Markov/ - Cambridge lecture notes on discrete-time Markov Chains
• https://link.springer.com/book/10.1007%2F978-3-319-97704-1 - book by E. Moulines et al, you are mostly interested in chapters 1,2,7 and 9 (book is accessible for download through HSE network)
• https://link.springer.com/book/10.1007%2F978-3-319-62226-2 - Stochastic Calculus by P. Baldi, good overview of conditional probabilities and expectations (part 4, also accessible through HSE network)
• https://link.springer.com/book/10.1007%2F978-1-4419-9634-3 - Probability for Statistics and Machine Learning by A. Dasgupta, chapter 19 (MCMC), also accessible through HSE network

Recommended literature (2nd term)

• https://link.springer.com/book/10.1007%2F978-1-4419-9634-3 - Probability for Statistics and Machine Learning by A. Dasgupta, chapter 12, 14
• https://link.springer.com/book/10.1007/978-3-540-68829-7 - Probability theory and Random Processes by L. Koralov and Y. Sinai, lecture 13 (Conditional expectations and martingales)
• https://link.springer.com/book/10.1007%2F978-3-319-62226-2 - Stochastic Calculus by P. Baldi - chapter 7,8 (Denis followed this book);
• http://th.if.uj.edu.pl/~gudowska/dydaktyka/Oksendal.pdf - Stochastic Differential Equations by B. Oksendal (another exposition of the stochastic calculus) - chapters 3-5;

Additional reading (Lecture from 14.12 and related topics)

• https://web.math.princeton.edu/~rvan/APC550.pdf- Ramon van Handel, Probability in High Dimension, chapter 2 (but I strongly recommend this book for your future course with Q. Paris, it is amazing);
• https://www.springer.com/gp/book/9783319002262 - Gentil, Barky, Ledoux. Classical book on Markovian semigroups, not very easy to read;