2023/2024

Markov Chains

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Andrey V. Dymov

Language: English

ECTS credits: 3

Contact hours: 30

Course Syllabus

Abstract

The simplest random process is a sequence of independent events (experiments). The scope of such processes is limited, since in practice very often the events are not independent. Markov chains are the simplest random processes formed by sequences of dependent events: given an event, it is assumed that the next event depends only on the given one, but does not depend on the previous events. In other words, «the future depends only on the present, but does not depend on the past». Markov chains have deep and beautiful but rather simple mathematics. Due to their amazing efficiency in applications to problems from various fields — mathematics, physics, computer science, biology, economics, etc. — they are known as probably the most important class of random processes. The present course is an introduction to the theory of Markov chains. We will discuss their most important properties and some of their applications PREREQUISITES: Standard courses of linear algebra and analysis of the first year of education. A standard course of the probability theory is recommended but not required: all essential knowledge from the probability theory will be communicated.