MAT5022 Stochastic Processes IBahçeşehir UniversityDegree Programs APPLIED MATHEMATICS (TURKISH, NON-THESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
APPLIED MATHEMATICS (TURKISH, NON-THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5022 Stochastic Processes I Fall
Spring
3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. İRİNİ DİMİTRİYADİS
Recommended Optional Program Components: None
Course Objectives: To provide the students with a fundemental understanding of stochastic processes.

Learning Outcomes

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.




Course Content

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.

Weekly Detailed Course Contents

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.

Sources

Course Notes / Textbooks: Sheldon Ross, Introduction to Probability Models, 8th edition, Academic Press, 2002.

Sheldon Ross, Stochastic Porcesses, 2nd edition, John Wiley and Sons, 1996.
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 6 % 20
Midterms 2 % 40
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Homework Assignments 6 13 78
Midterms 2 25 50
Final 1 30 30
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To apply mathematical principles to real world problems.
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.