COURSE UNIT TITLE

: STOCHASTIC PROCESSES

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 5015 STOCHASTIC PROCESSES ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR UMAY ZEYNEP UZUNOĞLU KOÇER

Offered to

Statistics (English)
STATISTICS (ENGLISH)
Statistics (English)

Course Objective

The aim of this course is to understand and apply stochastic processes at basic level. Besides it is aimed to provide the students with knowledge about how to analyze a system by using probability rules and stochastic processes, the characteristics and usage of the Markov chains and the Poisson process.

Learning Outcomes of the Course Unit

1   Defining basic preliminaries about stochastic processes
2   Formulating and expressing a system by using the characteristics of Bernoulli process, Markov chains or Poisson process
3   Performing calculations related with Bernoulli process and Markov chains
4   Performing calculations related with the random variable of Poisson process
5   Performing implementations of Markov chains and Poisson process
6   Reviewing the recent literature about Markov chains and Poisson processes and presenting examples

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Definition of random variable, expectation, moment generating functions, characteristic function and Laplace transforms.
2 Exponential distribution, memoryless property, some probability inequalities, limit theorems, definition and classification of stochastic processes
3 Discrete time stochastic processes: Bernoulli processes
4 Discrete time Markov chains, basic concepts, one step and n-step transition probabilities, canonical representation of transition matrix
5 Classification of states, steady state probabilities, transient state finite Markov chains
6 Examples on the applications of discrete time Markov chains
7 Examples on the applications of discrete time Markov chains
8 MIDTERM
9 Continuous time Markov chains, general concepts, Poisson precess definition, Presentation
10 Poisson process, relation with the exponential distribution and gamma distribution, Presentation
11 Pure birth process, pure death process, birth and death processes
12 Non-homogeneous Poisson process, Homework
13 Examples on the applications of continuous time Markov chains, Homework
14 Examples on the applications of continuous time Markov chains

Recomended or Required Reading

Textbook(s):
S. M. Ross, 2003, "Introduction to Probability Models", Academic Press, USA.

References:
S. M. Ross, 1996, "Stochastic Processes", Wiley Series in Probability and Statistics, New Jersey.

Materials: None

Planned Learning Activities and Teaching Methods

Lecture, problem solving, homework, presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 PRS PRESENTATION
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE MTE* 0.30 + ASG * 0.20 + PRS * 0.10 + FIN * 0.40
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE* 0.30 + ASG * 0.20 + PRS * 0.10 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of midterm, presentation, homework, and final exam.

Language of Instruction

English

Course Policies and Rules

Student responsibilities:
Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy.

Contact Details for the Lecturer(s)

DEU Fen Fakültesi Istatistik Bölümü
e-mail: umay.uzunoglu@deu.edu.tr
Tel: 0232 301 85 60

Office Hours

It will be announced when the course schedule of the faculty is determined.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparing assignments 2 20 40
Preparing presentations 2 10 20
Preparations before/after weekly lectures 14 4 56
Preparation for final exam 1 10 10
Preparation for midterm exam 1 20 20
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 192

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1555
LO.2555
LO.3555
LO.4555
LO.5555
LO.6555

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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