Stochastic analysis 2021 2022

Lecturers and Seminarists

Lecturer	Naumov Alexey	[anaumov@hse.ru]	T924
Seminarist	Samsonov Sergey	[svsamsonov@hse.ru]	T926

About the course

This page contains materials for Stochastic Analysis course in 2021/2022 year, mandatory one for 1st year Master students of the Statistical Learning Theory program (HSE and Skoltech).

Grading

The final grade consists of 3 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 + 0.1*O_{Bonus HW}

with the usual (arithmetical) rounding rule.

Table with grades

Lectures

• Lecture 11.09
• Lecture 27.11
• Lecture 11.12

Seminars

• Seminar 11.09
• Seminar 18.09
• Seminar 02.10 (first part, Gambler's ruin was not discussed here), Seminar 02.10 (second part, Dooob's optional sampling theorem (was provided without the proof) and Doob's maximal inequality)
• Seminar 09.10 (fist part, martingales), Seminar 09.10 (secoond part, Wiener process)
• Seminar 20.11Seminar 20.11 (video)
• Seminar 27.11Seminar 27.11 (video)

Homeworks

• Homework №1, deadline: 05.10.2021, 23:59 Hints
• Homework №2, deadline: 04.11.2021, 23:59Hints
• Homework №3, deadline: 12.12.2021, 23:59

Exam

• List of questions

Midterm

Midterm will take place on Saturday, 13.11.2020, at 11:00. Midterm is open-book, all materials are allowed. Midterm will take 3 hours and it will contain 6 problems. Solving any 5 of them will give you the maximal grade.

• List of topics
• Consultation, video, Consultation, notes

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;
• http://th.if.uj.edu.pl/~gudowska/dydaktyka/Oksendal.pdf - Stochastic Differential Equations by Bernt Oksendal, chapters 3-4-5 provide a construction of the Stochastic integral and all required information on SDE's.