Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
FMA707	ADVENCED STOCHASTIC PROCESSES	Compulsory	1	1	6

Level of Course Unit

Third Cycle

Objectives of the Course

The aims of this course is to learn the related concepts of Markov processes, i.e. continuous parameter Markov chains, parallel to that of discrete parameter Markov chains, To learn the concepts related to renewal, regenerative and Markov renewal processes

Name of Lecturer(s)

Doç. Dr. Selahattin MADEN

Learning Outcomes

1	To learn the related concepts of Markov processes, i.e. continuous parameter Markov chains, parallel to that of discrete parameter Markov

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

• Markov chains, visits to a fixed state, classification of states • Computation of R and F matrices • Recurrent states and the limiting probabilities, transient and periodic states • Branching processes, Potantials and excessive functions, optimal stopping • Markov processes, sample path behaviour, structure of a Markov process • Potantiels and generators, limit theorems • Markov renewal functions and classification of states • Markov renewal functions and classification of states.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Markov chains, visits to a fixed state, classification of states
2	Computation of R and F matrices
3	Recurrent states and the limiting probabilities, transient and periodic states
4	Branching processes
5	Potantiels and excessive functions, optimal stopping
6	Games with discounting and fees
7	Markov processes, sample path behaviour, structure of a Markov process
8	Mid-term exam
9	Potantiels and generators, limit theorems
10	Renewal Processes
11	Regenerative processes and renewal theory
12	Delayed and stationary processes
13	Delayed and stationary processes
14	Markov renewal functions and classification of states
15	Markov renewal functions and classification of states
16	End-of-term exam

Recommended or Required Reading

1 Çinlar E., 1975, introduction to Stochastic Processes, Englewood Cliffs, NJ, (Textbook). Other References 1 Karlin S., Taylor H.E., 1998, An introduction to Stocastic Processes.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	16	3	48
Problem Solving	12	5	60
Self Study	10	6	60
Individual Study for Homework Problems	10	6	60
Individual Study for Mid term Examination	8	5	40
Individual Study for Final Examination	6	5	30
TOTAL WORKLOAD (hours)			304

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	5

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High