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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| STATISTICS PR. | |
| Code | ISB419 |
| Name | Stochastic Processes |
| Term | 2026-2027 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SELAHATTİN KAÇIRANLAR |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The aim is to introduce the concept of randomness, to build stochastic models, and to understand some of the stochastic processes used in stochastic modeling
Course Content
This course covers the fundamentals of probability theory, random variables, conditional probability, and conditional distributions, in addition to the evaluation of Markov chains, exponential processes, and Poisson processes.
Course Precondition
no
Resources
Ross, S. M. (2000). Introduction to Probability Models, Seventh Edition, Academic Press.
Notes
Ross, S. M. (1996). Stochastic Processes , Second Edition, John Wiley and Sons, Inc. Çınlar, E. (1975). Introduction to Stochastic Processes, Prentice-Hall, Inc. Khaniyev, T. (2003). Markov Zincirleri, Karadeniz Teknik Üniversitesi Matbaası. Karlin, S. and Taylor, H.M. (1975) A First Course in Stochastic Processes Second, Academic Press.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | It creates exponential distribution models |
| LO02 | Describes Poisson processes |
| LO03 | learns waiting time distributions |
| LO04 | learns Markov chains |
| LO05 | calculates the transition probabilities |
| LO06 | learns the Chapman-Kolmogorov equations |
| LO07 | learns continuous time Markov chains |
| LO08 | learns renewal theory and its applications |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Statistics | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Make statistical inference (estimation, hypothesis tests etc.) | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques and gain insight | 5 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programs | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Probability spaces and some basic properties | reading source | Öğretim Yöntemleri: Anlatım |
| 2 | Extension theorem, Borel-Cantelli lemmas | reading source | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Random variables, random vectors, conditional distributions | reading source | Öğretim Yöntemleri: Anlatım |
| 4 | Expected Value and Moment Generating Function | reading source | Öğretim Yöntemleri: Anlatım |
| 5 | Stochastic processes, classification of stochastic processes | reading source | Öğretim Yöntemleri: Anlatım |
| 6 | Bernoulli processes | reading source | Öğretim Yöntemleri: Anlatım |
| 7 | The number and timing of successes in Bernoulli processes | reading source | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Reviewing the topics covered using lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Poisson processes | reading source | Öğretim Yöntemleri: Anlatım |
| 10 | Inter-destination and waiting time distributions in Poisson processes | reading source | Öğretim Yöntemleri: Anlatım |
| 11 | Markov chains, transition probabilities, and Chapman-Kolmogorov equations | reading source | Öğretim Yöntemleri: Anlatım |
| 12 | Limiting properties of Markov chains | reading source | Öğretim Yöntemleri: Anlatım |
| 13 | Applications of Markov chains | reading source | Öğretim Yöntemleri: Anlatım |
| 14 | Continuous parameter alien Markov chains | reading source | Öğretim Yöntemleri: Anlatım |
| 15 | birth and death processes | reading source | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Reviewing the topics covered using lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Reviewing the topics covered using lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 6 | 6 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 120 | ||
| Total Workload / 25 (h) | 4,80 | ||
| ECTS | 5 ECTS | ||