Master
2020/2021
Stochastic Processes
Type:
Elective course (Mathematics)
Area of studies:
Mathematics
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
2 year, 4 module
Mode of studies:
distance learning
Instructors:
Mauro Mariani
Master’s programme:
Mathematics
Language:
English
ECTS credits:
2
Contact hours:
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
Interim Assessment
- Interim assessment (4 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