Магистратура 2021/2022

Стохастические процессы

Статус: Курс по выбору (Математика и математическая физика)

Направление: 01.04.01. Математика

Кто читает: Факультет математики

Где читается: Факультет математики

Когда читается: 1-й курс, 4 модуль

Формат изучения: с онлайн-курсом

Онлайн-часы: 37

Охват аудитории: для своего кампуса

Преподаватели: Мариани Мауро

Прогр. обучения: Математика и математическая физика

Язык: английский

Кредиты: 2

Контактные часы: 2

Course Syllabus

Abstract

The purpose of this course is to teach students the theoretical and practical aspects of working with stochastic (random) processes, including those arising in Economics, technology and other fields. As a result of mastering the discipline the student must: * 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. Prerequisites to the discipline are mandatory courses of mathematical analysis and probability theory.

Learning Objectives

• to teach students the theoretical and practical aspects of working with stochastic (random) processes

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

Assessment Elements

• online course tests
• the oral exam
• online course tests
• the oral exam

Interim Assessment

• 2021/2022 4th module
  The final score consists of the average score for the online course tests (50%) and the score for the oral exam (50%).

Bibliography

Recommended Core Bibliography

• 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

Recommended Additional Bibliography

• 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