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FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES /
Katalog Ana Sayfa
  Katalog Ana Sayfa  KTÜ Ana Sayfa   Katalog Ana Sayfa
 
 

IST4013Stochastic Processes4+0+0ECTS:6
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of STATISTICS and COMPUTER SCIENCES
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 4 hours of lectures per week
LecturerProf. Dr. Zafer KÜÇÜK
Co-LecturerNone
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
Had students conceptualize the randomness as processes, giving the necessary knowledge of probability especially for stochastic modeling and analyzing this models, introducing some of the stochastic processes those are used in stochastic modeling.
 
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : learn random functions and stochastic process5,81,
LO - 2 : calculate numerical correlation function and expected stochastic value and its variance.5,81,
LO - 3 : learn the importance of conditions essential for the continuum, integral and derivation of stochastic process.5,81,
LO - 4 : receive theorical and practical information about stationary processes, processes with independent increment.5,81,
LO - 5 : receive skills about stochastic modelling under dependence condition.5,81,
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), LO : Learning Outcome

 
Contents of the Course
Random variables, random vectors, conditional distributions, expected value and probability calculations by conditioning, classification of stochastic processes, family of finite dimensional distributions, mean, variance, covariance correlation functions of stochastic processes, independent and stationary increment of processes, counting processes, Bernoulli processes and numbers and times of successes for the Bernoulli processes, Poisson processes, Markov chains, Markov property, transition probabilities and Chapman-Kolmogorov equations.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Probability spaces and its basic properties.
 Week 2Random variables, random vectors, conditional distributions, expected value and probability calculations by conditioning.
 Week 3Stochastic processes, classification of stochastic processes, trajectories, family of finite dimensional distributions, probability distribution on trajectory space and Kolmogorov existence theorem.
 Week 4Mean, variance, covariance correlation functions of stochastic processes, independent and stationary increment of processes.
 Week 5Counting processes, Bernoulli processes and numbers and times of successes for the Bernoulli processes.
 Week 6Poisson processes and their characterization
 Week 7Review and problem solved
 Week 8Mid-term exam
 Week 9Arrival times and waiting times distributions for the Poisson processes, conditional distribution of arrival times
 Week 10decomposition of Poisson processes into finite number of independent counting processes.
 Week 11 Markov chains, Markov property, transition probabilities and Chapman-Kolmogorov equations.
 Week 12Visiting a fixed state, distribution of the first visiting time and the number of visits of a state, classification of states.
 Week 13Asymptotic properties of Markow chains.
 Week 14Markov processes, Markov processes with two states, birth and death processes.
 Week 15Review and problem solved
 Week 16End-of-term exam
 
Textbook / Material
1Aliyev R., 2010; Stokastik Süreçler Teorisine Giriş, KTU Yayınları, Trabzon
 
Recommended Reading
1Çınlar E., 1997; Introduction to Stochastic Processes, Englewood Cliffs, N J.
2Karlin S., Taylor H. E., 1998; An Introduction to Stochastic Modeling, Academic Press.
3Khaniyev T., 2003; Markov Zincirleri, KTU Yayınları, Trabzon
4Ross S. M., 1993; Introduction to Probability Models, Academic Press Inc., New York
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 10/11/2021 1,5 50
End-of-term exam 16 02/01/2021 1,5 50
 
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 4 14 56
Sınıf dışı çalışma 5 14 70
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 20 1 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 15 1 15
Dönem sonu sınavı 2 1 2
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load165