Markov Chains

2025/2026

Учебный год

ENG

Обучение ведется на английском языке

3

Кредиты

Кто читает:

Департамент больших данных и информационного поиска

Статус:

Курс обязательный

Когда читается:

1-й курс, 2 модуль

Преподаватели

Самсонов Сергей Владимирович

Шешукова Марина Евгеньевна

Course Syllabus

Abstract

The course is an introduction to the theory of Markov chains, an area of modern probability theory widely used in applications. In this course, we will start from the theory of finite state space Markov chains and continue with the general case of Markov chains with arbitrary state space. We will cover various ergodicity results for Markov kernels and relations between them, central limit theorem for Markov chains, and applications of Markov chains. In terms of applications, we will consider the Markov Chain Monte Carlo methods and study some most classical examples of algorithms of this family.

Learning Objectives

• Purpose of course: understanding mathematical fundamentals of the Markov chains and their applications in machine learning models.

Expected Learning Outcomes

• The ability to apply Markov chains methodology to solve theoretical problems in related fields
• Ability to apply and analyze the Markov Chain Monte Carlo (MCMC) algorithms
• Developing the skill of problem-solving and understanding the theoretical concepts

Course Contents

• Finite state-space Markov Chains.
• Markov kernels. Basics of Markov Chains with general state space.
• Geometric ergodicity of general state-space markov kernels.
• Coupling methods
• Central limit theorems (CLTs) for Markov chains
• Applications: MCMC

Assessment Elements

• Homeworks
  Tasks for the topics covered in class
• Exam
  The oral exam includes the main topics covered in lectures and seminars.

Interim Assessment

• 2025/2026 2nd module
  0.5 * Exam + 0.5 * Homeworks

Bibliography

Recommended Core Bibliography

• Markov chains, Revuz, D., 2005

Recommended Additional Bibliography

• Meyn, S. P., & Tweedie, R. L. (2009). Markov Chains and Stochastic Stability (Vol. 2nd ed). Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=313161

Authors

• Emasheva Valeriia Anatolevna