Stochastic analysis 2020 2021

Lecturers and Seminarists

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

About the course

This page contains materials for Stochastic Analysis course in 2020/2021 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 and Seminars

• Lecture 05.09
• Lecture 12.09
• Lecture 19.09
• Seminar 19.09
• Lecture-Seminar 26.09, part 1 (Martingales)
• Lecture-Seminar 26.09, part 2 (Wiener process)
• Lecture 03.10
• Seminar 03.10
• Lecture 17.10
• Seminar 31.10
• Lectures on Markov chains
• Seminar 14.11
• Lecture 21.11
• Seminar 21.11
• Lecture 28.11
• Seminar 28.11
• Lecture 05.12
• Seminar 12.12

Homeworks

• Homework №1, deadline: 10.10.2020, 23:59
• Homework №2, deadline: 17.11.2020, 23:59
• Homework №3, deadline: 10.12.2020, 23:59
• Homework №4 (bonus), deadline: 23.12.2020, 23:59

Exam

• Exam 23.12

Midterm

Midterm will take place on Saturday, 07.11.2020, at 11:10. You are allowed to use your lectures and seminar notes, or any other notes or books, but NOT the laptops, mobile phones and other devices. Midterm will take 1.5 hours and it will contain 6 problems. Solving any 5 of them will give you the maximal grade.

• List of topics

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