| Teaching Staff
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| Language of Instruction |
Türkçe (Turkish) |
| Type Of Course |
Compulsory |
| Prerequisites |
No pre-requisite |
| Recommended Optional Programme Component |
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| Course Objectives |
Definitions stationary stochastic processes, independent increments etc. Using basic properties of Bernoulli, Poisson, and Markov chains. |
| Course Content |
Probability space and random variables. Expectations and independence. Bernoulli processes and sums of independent random variables. Poisson processes. Markov chains. Limiting behaviour and applications of Markov chains. Potantials, exclusive function and optimal stopping of Markov chains. |
| Learning Outcomes (LO) |
The student can solve stationary stochastic processes, independent increments etc. Using basic properties of Bernoulli, Poisson, and Markov chains. |
| Mode of Delivery |
Face to face |
| Course Outline |
| Week |
Topics |
| 1. Week |
Basic probability concepts |
| 2. Week |
Conditional probability and its properties |
| 3. Week |
Concepts of expectated values |
| 4. Week |
Bernoulli processes |
| 5. Week |
The process of success numbers |
| 6. Week |
Success times |
| 7. Week |
Sums of independent random variables, limiting behavior |
| 8. Week |
Poisson processes. |
| 9. Week |
Arrival times, repetition times |
| 10. Week |
Superposition of Poisson processes and the decomposition |
| 11. Week |
Markov chains |
| 12. Week |
Entering a fixed state, the first entry time and the classification of states |
| 13. Week |
Potentials, and the calculation of eventual transition matrices. |
| 14. Week |
Limiting behaviours and applications of Markov chains |
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| Assessment |
| |
Percentage(%) |
| Mid-term (%) |
40 |
| Quizes (%) |
|
| Homeworks/Term papers (%) |
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| Practice (%) |
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| Labs (%) |
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| Projects/Field Work (%) |
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| Seminars/Workshops (%) |
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| Final (%) |
60 |
| Other (%) |
|
| Total(%) |
100 |
|
| Course Book (s) and/or References |
1. Çınlar E., 1975, Introduction to Stochastic Processes, Englewood Cliffs, N J.
2. Ross, S.M., 1996, Stochastic Processes, JohnWiley&Sons.
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| Work Placement(s) |
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| The Relationship between Program Qualifications (PQ) and Course Learning Outcomes (LO) |
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