Stochastic Processes

2024/2025

Academic Year

RUS

Instruction in Russian

6

ECTS credits

Delivered at:

Department of Statistics and Data Analysis

Course type:

Elective course

When:

4 year, 1, 2 module

Программа дисциплины

Аннотация

The course on stochastic processes is aimed at students who are familiar with the basics of probability theory and who want to learn the basic concepts, theoretical facts and practical methods of working with random variables changing over time. Such quantities arise naturally in many applied fields while trying to describe objects whose behavior is influenced by a large number of factors that cannot be described by deterministic functions. The main objectives of the course are to introduce students to the most important types of random processes (Gaussian and Markov processes, Brownian motion, renewal processes, etc.) and mastering the basic methods of analysis and modeling of stochastic processes.

Цель освоения дисциплины

• The purpose of this course is to equip students with theoretical knowledge and practical skills, which are necessary for the analysis of stochastic dynamical systems in economics, engineering and other fields. More precisely, the objectives are 1. study of the basic concepts of the theory of stochastic processes; 2. introduction of the most important types of stochastic processes; 3. study of various properties and characteristics of processes; 4. study of the methods for describing and analyzing complex stochastic models.

Планируемые результаты обучения

• Know the basic concepts of the theory of stochastic processes Know the most important examples of stochastic processes and their properties Be able to apply methods of description and analysis of stochastic models in specific problems.

Содержание учебной дисциплины

• The renewal process
• Markov chain
• Poisson process
• Gaussian process
• Stationarity. Linear filter
• Ergodicity, continuity and differentiability
• Stochastic integration and ito formula
• The Levy Processes

Элементы контроля

• Первая контрольная работа
• Вторая контрольная работа
• Оценка за работу в течение семестра
• Итоговая контрольная работа

Промежуточная аттестация

• 2024/2025 2nd module
  0.2 * Вторая контрольная работа + 0.15 * Итоговая контрольная работа + 0.15 * Итоговая контрольная работа + 0.15 * Оценка за работу в течение семестра + 0.15 * Оценка за работу в течение семестра + 0.2 * Первая контрольная работа

Список литературы

Рекомендуемая основная литература

• Oliver Knill. (2009). Probability and Stochastic Processes with Applications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.286BE5CF

Рекомендуемая дополнительная литература

• Robert M. Gray, Elizabeth Dubois, Jordan Gray, R. Adm, Augustine Heard Gray, & Sara Jean Dubois. (2001). Probability, Random Processes, and Ergodic Properties. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.B2CBEC5E

Авторы

• Панов Владимир Александрович
• Сиротин Вячеслав Павлович