Stochastic Processes (MATH495) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Stochastic Processes MATH495 3 0 0 3 6
Pre-requisite Course(s)
Math 392 or Consent of the instructor
Course Language English
Course Type N/A
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.


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
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)
Special Course Internship
Field Work
Study Hours Out of Class 16 3 48
Presentation/Seminar Prepration
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