Бакалавриат
2023/2024
Стохастические процессы
Статус:
Курс по выбору (Фундаментальная и компьютерная лингвистика)
Направление:
45.03.03. Фундаментальная и прикладная лингвистика
Кто читает:
Школа лингвистики
Где читается:
Факультет гуманитарных наук
Когда читается:
4-й курс, 3 модуль
Формат изучения:
с онлайн-курсом
Онлайн-часы:
20
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Макарчук Илья Владимирович
Язык:
английский
Кредиты:
3
Контактные часы:
6
Course Syllabus
Abstract
The present course introduces the main concepts of the theory of stochastic processes and its applications. During the study, the students will get acquainted with various types of stochastic processes and learn to analyse their basic properties and characteristics. The material is anticipated to be of great interest for students willing to enhance their knowledge of stochastics and its use for the analysis of complex dynamical systems arising in various fields, such as economics or engineering.The main purpose of this course is to introduce the main concepts of the theory of stochastic processes and provide some ideas for its application to the solution of various problems in economics, finance, and other related fields.
Learning Objectives
- The main purpose of this course is to introduce the main concepts of the theory of stochastic processes and provide some ideas for its application to the solution of various problems in economics, finance, and other related fields.
Expected Learning Outcomes
- students can understand the basic notions of probability theory, which are needed for this course (probability space, convolution, Laplace transform)
- students can give a definition of a stochastic process
- student can understand the definitions and main properties of Poisson, non-homogeneous Poisson and compound Poisson processes
Course Contents
- Introduction & Renewal processes
- Poisson Processes
- Markov Chains
- Gaussian Processes
- Stationarity and Linear filters
- Ergodicity, differentiability, continuity
- Stochastic integration & Itô formula
- Lévy processes
Bibliography
Recommended Core Bibliography
- Oliver, Y. (2012). A Comprehensive Introduction to Stochastic Processes (Vol. 1st ed). Delhi: Orange Apple. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=406411
Recommended Additional Bibliography
- Chandra, T. K., & Gangopadhyay, S. (2018). Introduction to Stochastic Processes. New Delhi: Narosa Publishing House Pvt. Ltd. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2023979