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Bachelor 2020/2021

## Stochastic Process

Type: Elective course (Economics and Statistics)
Area of studies: Economics
When: 4 year, 3 module
Mode of studies: distance learning
Language: English
ECTS credits: 2

### Course Syllabus

#### Abstract

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.

#### Learning Objectives

• 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.

#### Expected Learning Outcomes

• 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.
• 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.

#### Course Contents

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

#### Assessment Elements

• Домашняя работа
• Итоговая контрольная работа
• Домашняя работа
• Итоговая контрольная работа

#### Interim Assessment

• Interim assessment (3 module)
0.3 * Домашняя работа + 0.7 * Итоговая контрольная работа