Graduate
Institute of Graduate Studies
Mathematics (PHD)
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Stochastic Processes

Course CodeSemester Course Name LE/RC/LA Course Type Language of Instruction ECTS
DMB0011 Stochastic Processes 3/0/0 DE Turkish 7
Course Goals This course aims to provide the definition and analysis of stochastic processes arised in financial applications.
Prerequisite(s) None.
Corequisite(s) None.
Special Requisite(s) The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s) Assist. Prof. Dr. Hikmet ÇAĞLAR
Course Assistant(s) None.
Schedule Will be announced in the forthcoming term.
Office Hour(s) Yrd. Doç. Dr. Hikmet ÇAĞLAR, AK/3-A-09.
Teaching Methods and Techniques Lecture and homeworks.
Principle Sources Stochastic Mechanics And Stochastic Processes 1988, A. Truman, I. M. Davies
Other Sources -
Course Schedules
Week Contents Learning Methods
1. Week Stochastic Processes: Definition and Classification Lecture and homework
2. Week Risk processes Lecture and homework
3. Week Poisson process Lecture and homework
4. Week Renewal processes Lecture and homework
5. Week Renewal processes Lecture and homework
6. Week Random walks Lecture and homework
7. Week Random walks Lecture and homework
8. Week Midterm Midterm
9. Week Markov Chains Lecture and homework
10. Week Markov Chains Lecture and homework
11. Week Continuous time Markov processes Lecture and homework
12. Week Martingale techniques Lecture and homework
13. Week Stochastic integrals and Ito’s formula Lecture and homework
14. Week Applications Computer Applications
15. Week Final Exam
16. Week Final Exam
17. Week Final Exam
Assessments
Evaluation tools Quantity Weight(%)
Midterm(s) 1 50
Final Exam 1 50


Program Outcomes
PO-1Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1◦will be able to define approximate stochastic process models and analyze them for a given research problem.
LO-2will be able to provide logical proofs of important theoratical results
LO-3◦will be able to apply the theory of stochastic processes to model real random phenomena.
LO-4◦will be able to analyse financial stochastic processes.
LO-5will be able to model real life financial stochastic processes.
Course Assessment Matrix:
Program Outcomes - Learning Outcomes Matrix
 PO 1PO 2PO 3PO 4PO 5PO 6PO 7PO 8PO 9
LO 1
LO 2
LO 3
LO 4
LO 5