Description of Individual Course Units
Course Unit CodeCourse Unit TitleType of Course UnitYear of StudySemesterNumber of ECTS Credits
İST302STOCHASTIC PROCESSESCompulsory367
Level of Course Unit
First Cycle
Objectives of the Course
Theory and inferences of stocastic modelling will be examined and some applications will be carried.
Name of Lecturer(s)
Assoc. Prof. Dr. Halil TANIL
Learning Outcomes
1To get the one step transition probability matrix of a markov chain.
2To construct the transition diagram of a markov chain.
3To get the joint and conditional probability function ina markov chain.
4To compute the probabilities of events in a markov chain.
5To compute the n-step transition probability matrix by using the one step transition probability matrix.
6To determine the type of every condition in a state space.
7To compute the probabilty to be caught for any given markov chain.
8To compute the average time of caught of any given markov chain.
9To compute the average time of visit for every state for any given markov chain.
10The concept of Random Walk which is a special markov chain.
11To decide whether there is a limit distribution of a markov chain or not.
12To get the limit distribution of a markov chain if exists.
13To classify the markov chains.
14The concept of Poisson Process.
15To determine the difference between homogeneus and nonhomogeneus Poisson Processes.
16To describe a poisson process for a suitable problem.
17The concept of stochastic process.
18To write the state space and parameter space of any given stochastic process.
19To classify stochastic processes.
20The concept of Markov Chain.
Mode of Delivery
Face to Face
Prerequisites and co-requisities
None
Recommended Optional Programme Components
None
Course Contents
Introduction to Stocastic Processes. Definitions and Concepts. Stocastic Systems. Markov Processes. Markov Chains. First Step Analysis. Random Walk Theorem. Poisson Processes. Distributions Related to Poisson Processes. Renewal Process. Birth-Death Processes.
Weekly Detailed Course Contents
WeekTheoreticalPracticeLaboratory
1Definition of Stochastic Process. Basic Concepts. Classifying Stocastic Processes.
2Markov process. Markov chain. One step and n-step transition probability matrices.
3Types of states. Joint and conditional distributions of markov chains. Homework 1
4Probabilities of being caught. Average caught time.
5Average visit counts. Classic an done step solutions.
6Random walk. Probabilities of being caught. Homework 2
7Control of regularity in Markov chains and limit distribution.
8Reducibility in markov chains. Quiz1
9Midterm exam
10Period in markov chains. Homework 3
11Temporary and comeback states in markov chains with zero probabilty of being caught. Probability of comeback. Average count of comeback to one specific state.
12Poisson Processes.
13Nonhomogenous poisson rocesses. Homework 4
14Continuous markov chains.
15Renewal process. Birth process. Death process. Quiz 2
16Final exam.
Recommended or Required Reading
1. Papoulis, A., 1991. “Probability, random variables and stochastic processes”. New York : McGraw-Hill. 2. Ross, S. M., 2000. “Introduction to Probability Models”. Sixth Edition. 3. Taylor, H. M., Karlin, S., 2001. “An Introduction to Stochastic Modeling”. Academic Press, Third Edition.
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Term (or Year) Learning ActivitiesQuantityWeight
SUM0
End Of Term (or Year) Learning ActivitiesQuantityWeight
SUM0
SUM0
Language of Instruction
Turkish
Work Placement(s)
None
Workload Calculation
ActivitiesNumberTime (hours)Total Work Load (hours)
Midterm Examination122
Final Examination122
Quiz212
Attending Lectures14456
Individual Study for Homework Problems4520
Individual Study for Mid term Examination14040
Individual Study for Final Examination15050
Individual Study for Quiz21530
TOTAL WORKLOAD (hours)202
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Ege University, Bornova - İzmir / TURKEY • Phone: +90 232 311 10 10 • e-mail: intrec@mail.ege.edu.tr