Stochastic Processes (MATH495) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Stochastic Processes	MATH495	Area Elective	3	0	0	3	6

Pre-requisite Course(s)
MATH392

Course Language	English
Course Type	Elective Courses
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)	Prof. Dr. Sofiya Ostrovska Asst. Prof. Dr. Ümit Aksoy
Course Assistants
Course Objectives	This course is intended primarily for the student of mathematics, physics or engineering who wishes to learn the notion of stochastic processes and get familiar with their common applications.
Course Learning Outcomes	The students who succeeded in this course; At the end of the course the students are expected to: 1) Know the properties and usage of special probability distributions such as Erlang, Weibull, hypoexponential. 2) Understand the notion of stochastic process and analyze different types of stochastic processes. 3) know the Poisson process, its properties, applications and generalizations. 4) classify states and compute probabilities for Markov Chains 5) Model different real-life situations with the help of stochastic processes.
Course Content	Basic notions of probability theory; reliability theory; notion of a stochastic process; Poisson processes, Markov chains; Markov decision processes.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Preliminaries: Probability, random events and random variables. Independence.	pp. 1 - 10
2	Classical probability distributions, their properties. Random vectors. Coditional distribution and conditional expectation.	pp. 11 -14
3	Reliability theory. Finding reliability function for different systems. Redundancy.	[1], pp. 29-33,pp 124-135.
4	Hazard rate function, the mean time to failure.	[1], pp. 228-236
5	Definition and examples of stochastic processes, their types.	pp. 26-27, [1], pp. 294-300
6	The Bernoulli and Poisson processes. Interarrival and waiting times.	pp. 31-36
7	Non-homogeneous and compound Poisson processes. Midterm I	pp. 46 - 49
8	Renewal processes. Erlang process. Renewal theorems.	pp. 55-60
9	Markov chains: Markov property, transition probabilities, transition graph. The Chapman-Kolmogorov equations.Computation of n-th step transition probabilities.	pp. 100-103
10	Classification of states and limiting probabilities. Equlibrium.	pp. 104-110
11	Absorbing Markov chains. Fundamental matrix.	[1], pp. 392-402
12	Midterm II. Continuous-time Markov chains. Kolmogorov’s equations.	pp.141-150
13	Time reversibility.	pp. 156-158
14	Applications of Markov chains.	pp. 118-122
15	Review.
16	Final exam.

Sources

Course Book	1. Sheldon M. Ross, Stochastic processes, Wiley, 1983.
Other Sources	2. K. S. Trivedi, Probability and Statistics with Reliability, Queueing, and Computer Science Applications, 2nd Edition, Wiley, 2002.
	3. J. G. Kemeny and J. L. Snell, Finite Markov chains, Springer, 1976.
	4. S. Karlin, H. M. Taylor, A first course in stochastic processes, 2-nd Ed, Academic Press, 1975.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	4	20
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	40
Final Exam/Final Jury	1	40
Toplam	7	100

Percentage of Semester Work
Percentage of Final Work	100
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Acquiring the skills of understanding, explaining, and using the fundamental concepts and methods of economics
2	Acquiring the skills of macro level economic analysis
3	Acquiring the skills of micro level economic analysis
4	Understanding the formulation and implementation of economic policies at the local, national, regional, and/or global level
5	Learning different approaches on economic and related issues
6	Acquiring the quantitative and/or qualitative techniques in economic analysis
7	Improving the ability to use the modern software, hardware and/or technological devices
8	Developing intra-disciplinary and inter-disciplinary team work skills					X
9	Acquiring an open-minded behavior through encouraging critical analysis, discussions, and/or life-long learning
10	Adopting work ethic and social responsibility
11	Developing the skills of communication.
12	Improving the ability to effectively implement the knowledge and skills in at least one of the following areas: economic policy, public policy, international economic relations, industrial relations, monetary and financial affairs.

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	16	3	48
Presentation/Seminar Prepration
Project
Report
Homework Assignments	4	10	40
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	12	24
Prepration of Final Exams/Final Jury	1	18	18
Total Workload			130