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Bachelor 2023/2024

# Stochastic Processes

Area of studies: Fundamental and Applied Linguistics
Delivered by: School of Linguistics
When: 4 year, 3 module
Mode of studies: distance learning
Online hours: 20
Open to: students of all HSE University campuses
Instructors: Ilya Makarchuk
Language: English
ECTS credits: 3
Contact hours: 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

• Final exam
• Homework

#### Interim Assessment

• 2023/2024 3rd module

#### 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