2026/2027
Цепи Маркова
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Мариани Мауро
Язык:
английский
Кредиты:
6
Контактные часы:
60
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.
Learning Objectives
- Learning the audience what are the Markov chains with finite number of states and the corresponding basic technique.
- Learning possible types of large-time behavior of the Markov chains with finite number of states.
- Learning some applications of the Markov chains technique to various examples arising in different areas.
Expected Learning Outcomes
- Learning about interpretation of the strong Markov property and applications.
- Evaluate speed of convergence from spectral and coupling methods
- Learn to evaluate and design an MCMC algorithm
Course Contents
- Introduction to Markov Chains
- Convergence to the Invariant Measure
- Monte Carlo Markov Chains
Assessment Elements
- Control Worksin class control works. 3 quick controls, very basic. 1 control during the fall session
- Oral exam
Interim Assessment
- 2026/2027 1st module1 * Control Works
- 2026/2027 2nd module0.5 * Oral exam + 0.5 * Control Works
