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:
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 |
|
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 |
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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
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.