Stochastic Processes (MAE532)

Undergraduate Courses Outlines - Department of Mathematics

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)	http://users.uoi.gr/abatsidis/532.html

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.

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

Books in English

• Lawler. Introduction to Stochastic Processes
• Ross. Introduction to probability models (Chapters 4, 6, 7)

Books in Greek:

• Χρήστος Λάγκαρης. Θεωρία Στοχαστικών διαδικασιών. Πανεπιστημιακό Τυπογραφείο Ιωαννίνων.
• Στοχαστικές Ανελίξεις , Κάκουλλος Θεόφιλος
• Στοχαστικές ανελίξεις, Δάρας Τρύφων Ι., Σύψας Παναγιώτης Θ.
• Στοχαστικές μέθοδοι στις επιχειρησιακές έρευνες, Βασιλείου Παναγιώτης - Χρήστος Μαθήματα στοχαστικών διαδικασιών Τ.Α., Αρτίκης Θεόδωρος Π.