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Course Syllabus

Course Syllabus


 

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Master 2021/2022

Stochastic Processes

Type: Elective course (Mathematics and Mathematical Physics)
Area of studies: Mathematics
Delivered by: Faculty of Mathematics
Where: Faculty of Mathematics
When: 1 year, 4 module
Mode of studies: distance learning
Online hours: 37
Open to: students of one campus
Instructors: Mauro Mariani
Master’s programme: Mathematics and Mathematical Physics
Language: English
ECTS credits: 2
Contact hours: 2

Course Syllabus

Full SyllabusAsk Question

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

Learning Objectives

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

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

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

Assessment Elements

  • non-blocking online course tests
  • non-blocking the oral exam
  • non-blocking online course tests
  • non-blocking the oral exam
Interim Assessment

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

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