Stochastic Processes

2023/2024

Academic Year

ENG

Instruction in English

3

ECTS credits

Delivered at:

School of Linguistics

Course type:

Elective course

When:

3 year, 4 module

Instructor

Makarchuk, Ilya

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

Assessment Elements

• Final exam
• Homework

Interim Assessment

• 2023/2024 4th module
  The final grade is the grade for the online course.

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

Authors

• LANDER Iurii ALEKSANDROVICH