Course Name Code Semester T+U Hours Credit ECTS
The Theory Of Stocastic Processes MAT 605 0 3 + 0 3 6
Precondition Courses Students are assumed to be familiar with Analysis I-II, Linear Algebra I-II, and Probability
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. HALİM ÖZDEMİR
Course Lecturers
Course Assistants Res.Asssist. Emre Kişi and Res.Assist. Tuğba Petik
Course Category Field Proper Education
Course Objective In the modern approach to stochastic processes, the primary object is the behavior of sample paths. This is especially so for the applied scientist and engineer, since it is the sample path which he observes and tries to control. Considerations in this course construct the bridge between mathematician and applied scientist.
Course Content Probability spaces and random variables. Expectations and independence. Bernoulli processes and sums of independent random variables. Poisson processes. Markov chains. Limiting behavior. Applications of Markov chains. Markov processes.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she consolidates the concept of probability Lecture, Question-Answer, Testing, Homework,
2 He/she consolidates the concept of random variables Lecture, Question-Answer, Self Study, Testing, Homework,
3 He/she understands the concept of expected value and independence Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Project / Design,
4 He/she sees some stochastic processes Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Project / Design,
5 He/she applies some stochastic processes Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Project / Design,
6 He/she constructs the bridge between mathematics and daily life. Lecture, Question-Answer, Drilland Practice, Self Study, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Probability spaces and random variables [1] pages 1-21
2 Expectations and independence [1] pages 21-43
3 Bernoulli processes and sums of independent random variables [1] pages 43-70
4 Bernoulli processes and sums of independent random variables (continuation) [1] pages 43-70
5 Poisson processes [1] pages 70-106
6 Poisson processes (continuation) [1] pages 70-106
7 Markov chains [1] pages 106-144
8 Markov chains (continuation) [1] pages 106-144
9 Limiting behavior [1] pages 144-169
10 Limiting behavior (continuation) [1] pages 144-169
11 Applications of Markov chains [1] pages 169-194
12 Applications of Markov chains (continuation) [1] pages 169-194
13 Markov processes [1] pages 232-282
14 Markov processes (continuation) [1] pages 232-282
Resources
Course Notes [1] Çınlar, E., Introduction to stochastic processes, Prentice-Holl, Inc., New Jersey, 1975.
Course Resources [2] Brzezniak, Z. and Zastawniak, T., Basic Stochastic Processes, Springer-Verlag, New York, 1998.>

[3] Hoel, P. G., Port, S. C. and Stone, C. J., Introduction to stochastic processes, University of California, Los Angeles, 1993.
Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Performans Görevi (Seminer) 40
1. Ödev 20
1. Ara Sınav 40
Total 100
1. Final 40
1. Yıl İçinin Başarıya 60
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 15 15
Assignment 1 8 8
Performance Task (Seminar) 1 20 20
Final examination 1 20 20
Total Workload 159
Total Workload / 25 (Hours) 6.36
dersAKTSKredisi 6