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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Doctorate
Course Catalog
http://www.fbe.ktu.edu.tr/
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FBE
GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS / Doctorate
Katalog Ana Sayfa
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MAT7343Advanced Stochastic Processes3+0+0ECTS:7.5
Year / SemesterSpring Semester
Level of CourseThird Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 3 hours of lectures per week
LecturerProf. Dr. Tülay YAZIR
Co-LecturerProf. Dr. İhsan Ünver
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
The aim of this course is to give information about the foundation of the stochastic processes and study the basic classes of the stochastic processes.
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : learn definition and classification of stochastic processes.1,2,3,4,5,61,3
PO - 2 : learn Poisson and Winer processes and to apply these processes to problems.1,2,3,4,5,61,3
PO - 3 : learn Markov processes and semi-Markov processes and to apply these processes to problems.1,2,3,4,5,61,3
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome

 
Contents of the Course
Random functions; definition and classifications of stochastic processes, fundamental characteristics of stochastic processes;stochastic processes with independent increments, Poisson and Winer processes, Markov processes and semi-Markov processes
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Random functions and stochastic processes: definitions, properties.
 Week 2 Fundamental characteristics of stochastic processes.
 Week 3Continuity, derivative and integral of stochastic processes.
 Week 4Stationary processes: definitions, properties and examples.
 Week 5Spectral density function:definitions and examples.
 Week 6Existence of the derivative and integral of stationary processes.
 Week 7Process with independent increment: Poisson and Wiener processes. Mathematical expectation, varyans, correlation function of this processes.
 Week 8Mid-term exam
 Week 9Renewal processes: definitions and properties
 Week 10Analytical and asymptotic results for the renewal function
 Week 11Markov process and Markov chains, classification of states and limit theorems
 Week 12Markov chains having two states, transition function and initial distribution, examples
 Week 13Transient and recurrent states
 Week 14Classification of state and martingales
 Week 15Birth and death chain,applications to birth and death chain.
 Week 16End-of-term exam
 
Textbook / Material
1Ross, S. M.,1993; Introduction to Probability Models, Academic Press, New york.
2Borovkov, A. A., 1976; Stochastic Process İn Queueing Theory, Springer-Verlang.
 
Recommended Reading
1Ceylan İnal H. , 1988; Olasılıksal süreçlere giriş: (Markov zincirleri), Ankara.
2Feller W., 1971; An Introduction to Probability Theory and Its Appl. II, J. Wiley, New york.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 11 27/11/2017 2 30
Quiz 7 20/12/2017 1 30
End-of-term exam 16 08/01/2018 2 40
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 3 14 42
Sınıf dışı çalışma 10 14 140
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 5 4 20
Arasınav 2 1 2
Uygulama 0 0 0
Klinik Uygulama 0 0 0
Ödev 0 0 0
Proje 0 0 0
Kısa sınav 0 0 0
Dönem sonu sınavı için hazırlık 5 3 15
Dönem sonu sınavı 2 1 2
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load221