Ondokuz Mayıs Üniversitesi Bilgi Paketi - Ders Kataloğu

Description of Individual Course Units

Course Unit CodeCourse Unit TitleType of CourseYearSemesterECTS
İST457 Stochastic Processes I 927006 4 7 5
Level of Course Unit
First Cycle
Objectives of the Course
Investigation of thestochasticprocesses, whicharethe general state of therandomvariableconcept, accordingtothestatespacesandindexclusters.
Name of Lecturer(s)
Prof. Dr. Vedat SAĞLAM
Learning Outcomes
  1. The student learns the relation between random variable and stochastic processes, state space, indices and stochastic function concepts with the help of this course
  2. Counting process, Wiener process, renewal process and awarded renewal process are given in this course. Data collection tools, data editing and presentation.
  3. The theory of Poisson process and its properties and current applications are explained.
  4. Markov chain, stochastic matrix and the establishment of double stochastic matrix are taught.
Mode of Delivery
Formal Education
Prerequisites and co-requisities
Probability I and Probebility II
Recommended Optional Programme Components
None
Recommended or Required Reading
1. C.İnal, Olasılıksal Süreçlere Giriş.H.Ü. Yayınları, Ankara,1998.
2. H.Hsu, Probability, RandomVariables, Randomprocesses. Shaum'sOutlines Series, 1996.
3. S.M.Ross, IntroductiontoProbabilityModels, ElsevierScience, USA, 2003.
Planned Learning Activities and Teaching Methods
Language of Instruction
Turkish
Work Placement(s)
None
Course Contents
Basic definitions of stochastic processes. Poisson process and its properties. Markov Chains with cut-off parameters
Weekly Detailed Course Contents
Week Theoretical Practice Laboratory
1.Defining the random variable and stochastic process.
2.Stationary process and homogenouos processes.
3.Counting process, Bernoulli process, geometric process, Wiener process, renewal process.
4.Poisson process, the expected value, variance and covariance of this process.
5.Properties of poisson process.
6.Applications of Poisson process.
7.Application of Poisson process on service channels.
8.Midterm exam
9.Markov chains in discrete paramters and in discrete space state.
10.Transition probabilities, probability vector and stochastic matrice.
11.The methods of finding n-steps stochastic matrice.
12.Obtaining Chapman-Kolmogorov equality and application of this equality.
13.Branching processes
14.Genereting function in branhing processes and calculating the expected value and variance.
15.
16.
Assessment Methods and Criteria
Term (or Year) Learning ActivitiesQuantityWeight (%)
Midterm Examination0100
SUM0
End Of Term (or Year) Learning ActivitiesQuantityWeight (%)
Final Examination0100
SUM0
Term (or Year) Learning Activities40
End Of Term (or Year) Learning Activities60
SUM100
Workload Calculation
ActivitiesQuantityTime(hours)Total Workload(hours)
Midterm Examination122
Final Examination122
Attending Lectures13339
Practice10220
Problem Solving10220
Question-Answer10220
Self Study428
Individual Study for Mid term Examination133
Individual Study for Final Examination133
Homework248
SUM125