MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5022 | Stochastic Processes I | Fall | 3 | 0 | 3 | 12 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Prof. Dr. İRİNİ DİMİTRİYADİS |
Course Objectives: | To provide the students with a fundemental understanding of stochastic processes. |
The students who have succeeded in this course; Students will be able to evaluate the statistical properties of random variables handle probabilistic transformations. Students will become familiar with stationary and nonstationary stochastic processes, and will know about areas of application with special attention given to finance. Students will know the application of Monte Carlo simulation. |
Short review of probability theory, counting processes; Markov processes and Kolmogorov equations; Brownian motion and geometric Brownian motion, Ito's lemma, Monte Carlo Simulation. Areas of application. |
Week | Subject | Related Preparation | |
1) | Review of probability, conditional probabilities and expectations. | ||
2) | Basic ideas about stochastic processes. Discrete time Markov chains, transition probabilities, classification of states, limiting probabilities. | ||
3) | Applications of Markov Chains, branching processes and Markov decision processes. | ||
4) | The exponential distribution and the Poisson process. Interrarival and waiting time distributions, nonhomogeneous and compound Poisson processes. | ||
5) | Continuous time Markov chains, birth and death processes, the Kolmogorov differential equations. | ||
6) | Limiting probabilities, time reversibility. Examples. | ||
7) | Renewal theory and its applications. | ||
8) | Martingales; definition, examples, the Optional Sampling Theorem and its applications. | ||
9) | Brownian motion, hitting times, the Gambler's ruin problem. | ||
10) | Geometric brownian motion and its application to finance. Pricing stock options, the arbitrage theorem. | ||
11) | The Black Scholes option pricing formula, gaussian processes. | ||
12) | Stationary and diffusion processes, examples. | ||
13) | The Ito Stochastic integral and the Ito formula and other stochastic integrals. | ||
14) | Monte Carlo Simulation. |
Course Notes: | Sheldon Ross, Introduction to Probability Models, 8th edition, Academic Press, 2002. Sheldon Ross, Stochastic Porcesses, 2nd edition, John Wiley and Sons, 1996. |
References: |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | % 0 | |
Homework Assignments | 6 | % 20 |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 2 | % 40 |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 0 | 0 | 0 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 6 | 13 | 78 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 2 | 25 | 50 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 30 | 30 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |