# Stochastic Processes (MAE532)

### General

School School of Science Department of Mathematics Undergraduate ΜΑΕ532 5 Stochastic Processes Lectures (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek Yes (in English, reading Course) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes The term "stochastic" is used to describe phenomena in which some randomness inherent. A stochastic process is a probabilistic model that describes the behaviour of a system that randomly evolves over time. Observing the system at discrete points in time (for instance at the end of each day or at the end of a time period, etc.) one gets a discrete time stochastic process. Observing the system continuously through time one gets a continuous time stochastic process. Objectives of the course are: Understanding the behaviour of a real system and based on its study to derive reliable results, a careful analysis of the model and the calculation of the results. A variety of classes of stochastic processes such as, the random walk, the Markov chains etc is used. The student should be able to understand the meaning of the stochastic process, use the Markov processes for modelling systems and become familiar with their application, and be able to make various calculations and appropriate conclusions when the stochastic process describes a specific applied problem. 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
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:

• R. Dobrow. Introduction to Stochastic Processes with R, Wiley, 2016.
• R. Durret. Essentials of Stochastic Processes, Springer, 3rd edition, 2016.
• V.G. Kulkarni. Modeling and Analysis of Stochastic Systems, 3rd edition, CRC Press, London 2017.
• N. Privault. Understanding Markov Chains [electronic resource] HEAL-Link Springer ebooks, 2013 (Κωδικός Εύδοξου: 73260010).
• M. Pinksy, S. Karlin. An introduction to stochastic modelling, 4th edition, Academic Press, 2011.
• S. Ross. Introduction to probability models, Academic Press, New York, 2014.
• [Περιοδικό / Journal] Stochastic Processes and their Applications (Elsevier)
• [Περιοδικό / Journal] Stochastics (Taylor - Francis)
• [Περιοδικό / Journal] Journal of Applied Probability (Cambridge University Press)