Description of Individual Course Units
 Course Unit Code Course Unit Title Type of Course Unit Year of Study Semester Number of ECTS Credits İST302 STOCHASTIC PROCESSES Compulsory 3 6 7
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
 1 To get the one step transition probability matrix of a markov chain. 2 To construct the transition diagram of a markov chain. 3 To get the joint and conditional probability function ina markov chain. 4 To compute the probabilities of events in a markov chain. 5 To compute the n-step transition probability matrix by using the one step transition probability matrix. 6 To determine the type of every condition in a state space. 7 To compute the probabilty to be caught for any given markov chain. 8 To compute the average time of caught of any given markov chain. 9 To compute the average time of visit for every state for any given markov chain. 10 The concept of Random Walk which is a special markov chain. 11 To decide whether there is a limit distribution of a markov chain or not. 12 To get the limit distribution of a markov chain if exists. 13 To classify the markov chains. 14 The concept of Poisson Process. 15 To determine the difference between homogeneus and nonhomogeneus Poisson Processes. 16 To describe a poisson process for a suitable problem. 17 The concept of stochastic process. 18 To write the state space and parameter space of any given stochastic process. 19 To classify stochastic processes. 20 The 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
 Week Theoretical Practice Laboratory 1 Definition of Stochastic Process. Basic Concepts. Classifying Stocastic Processes. 2 Markov process. Markov chain. One step and n-step transition probability matrices. 3 Types of states. Joint and conditional distributions of markov chains. Homework 1 4 Probabilities of being caught. Average caught time. 5 Average visit counts. Classic an done step solutions. 6 Random walk. Probabilities of being caught. Homework 2 7 Control of regularity in Markov chains and limit distribution. 8 Reducibility in markov chains. Quiz1 9 Midterm exam 10 Period in markov chains. Homework 3 11 Temporary and comeback states in markov chains with zero probabilty of being caught. Probability of comeback. Average count of comeback to one specific state. 12 Poisson Processes. 13 Nonhomogenous poisson rocesses. Homework 4 14 Continuous markov chains. 15 Renewal process. Birth process. Death process. Quiz 2 16 Final exam.
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 Activities Quantity Weight SUM 0 End Of Term (or Year) Learning Activities Quantity Weight SUM 0 SUM 0
Language of Instruction
Turkish
Work Placement(s)
None