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	-
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: Become familiar with the general theory and techniques related to Discrete Time Markov Chains (DTMC), and Continuous Time Markov Chains (CTMC). Become familiar with the concept of stochastic modelling. At the end of the course, the student will be able to: To develop aptitude in analyzing random walks. To have insight into Markov chains, Markov processes and birth-and-death processes, and to be able to determine their stationary distribution. To have a thorough understanding of the properties of the Poisson process. To get a feeling for the application of stochastic processes in the analysis and optimization of all kinds of systems and phenomena in industry and society. • 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

Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

Syllabus

Random Walk: Simple random walk, absorbing barriers, reflecting barriers. Markov Chains: General definitions, classification of states, limit theorems, irreducible chains. Markov Processes: The birth-death process. 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	Activity Semester Workload Lectures 39 Working independently 78 Exercises-Homeworks 33 Course total 150
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.