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	Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area
2	Can apply gained knowledge and problem solving abilities in inter-disciplinary research
3	Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary
4	Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study
5	Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework
6	Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility
7	Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation
8	To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2)
9	Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge
10	Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach.
11	Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

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