Stochastic Processes (MAE532)
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
ΜΑΕ532 |
| Semester |
5 |
| Course Title |
Stochastic Processes |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | It is desirable to have elementary knowledge of probability theory. |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
A stochastic process is a collection of random variables which describe the behavior of a system that evolves randomly in time. In this course you will gain the theoretical knowledge and practical skills necessary for the analysis of stochastic systems, i.e., systems that evolving over time under probabilistic laws. Stochastic modelling is an interesting and challenging area in applied probability that is widely used in physics, biology, engineering, as well as economics, finance, and social sciences. Our aim in this course is to provide an introduction in the basic notions of stochastic processes at an undergraduate level, with particular emphasis on the Markovian processes in discrete and in continuous time with discrete state spaces. The course aims to enable students to:
At the end of the course, the student will be able to:
• To be able to treat a modeling problem of moderate size in the area of stochastics. • Derive the theoretical properties of Markovian models and carry out corresponding calculations. |
|---|---|
| General Competences |
|
Syllabus
Introduction to stochastic processes: Definition, examples, Random walks: Constrained random walks: gambling problems, Reflected random walks, Discrete Time Markov Chains (DTMC): Introduction, Definitions, examples, Transient behaviour, First passage times, First step analysis, Classification of states, visits to a fixed state, limiting behaviour and applications, Continuous Time Markov Chains (CTMC): Poisson process and applications, Birth-death processes and applications.
Teaching and Learning Methods - Evaluation
| Delivery |
Classroom (face-to-face) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | -
Use of ICT in communication with students | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- V.G. Kulkarni. Introduction to Modeling and Analysis of Stochastic Systems Second Edition, Springer, 2011 (parts from Ch. 1-4).
- M. Pinsky, S. Karlin. An Introduction to Stochastic Modeling, Fourth Edition, Academic Press, 2011. (parts from Ch. 3-6).
- N. Privault. Understanding Markov Chains Examples and Applications. Springer, 2018.
- Ross, S.. Introduction to Probability Models, Academic Press, New York, 12th Ed. 2019.