2026/2027
Введение в теорию случайных процессов
ID 1249620
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Бланк Михаил Львович
Язык:
английский
Кредиты:
3
Контактные часы:
36
Course Syllabus
Abstract
The course is a continuation of the standard course in probability theory (associated mainly
with combinatorics) and is intended for an initial introduction to the theory of random processes. Particular
attention is paid to the connection of this theory with functional analysis and general measure theory, and
especially to various counterexamples. The course is aimed at 3rd-4th year bachelors, masters and postgraduates.
Learning Objectives
- The goal of the course is to master the rigorous mathematical framework of random process theory based on measure theory and functional analysis for working with continuous stochastic systems.
Expected Learning Outcomes
- knowledge of the fundamental principles of random process theory and the ability to apply them to solve problems
Course Contents
- The concept of a random process. Antagonistic/cooperative games.
- Elements of random analysis.
- Correlation theory of random processes.
- Markov processes with discrete and continuous time
- Wiener and Poisson processes.
- Stochastic integral. Ito’s formula.
- (sub/super) martingales.
- Infinitesimal semigroup operator.
- Stochastic stability of dynamical systems.
- Large deviations in Markov processes and chaotic dynamics.
- Nonlinear Markov processes.
Interim Assessment
- 2026/2027 4th moduleGrading: 0.4*(cumulative assessment) + 0.6*exam. The cumulative assessment is determined by written tests, delivery of sheets and work at lectures. Round up
Bibliography
Recommended Core Bibliography
- Krylov, N. V. (2002). Introduction to the Theory of Random Processes. Providence: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=971029
- Вероятность -. Кн.1: Вероятность - 1 : элементарная теория вероятностей. Математические основания. Предельные теоремы, Ширяев, А. Н., 2007
- Курс теории случайных процессов : учеб. пособие для мех.- мат. фак-тов ун-тов, Вентцель, А. Д., 1975
- Стохастические дифференциальные уравнения : введение в теорию и приложения, Оксендаль, Б., 2003
Recommended Additional Bibliography
- Chaumont, L., & Yor, M. (2012). Exercises in Probability : A Guided Tour From Measure Theory to Random Processes, Via Conditioning (Vol. 2nd ed). Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=466664
- Probability and random processes, Grimmett, G. R., 2020
- Statistics of random processes. Vol.2: Applications, Liptser, R. S., 2001