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School of Science
Department of Mathematics
|Level of Studies||
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|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.|
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.
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
|Use of Information and Communications Technology||-
Use of ICT in communication with students
|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.
- 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)