COURSE UNIT TITLE

: ADVANCED STOCHASTIC PROCESSES

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 6018 ADVANCED 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 give the students, who have the theoretical and practical knowledge about stochastic processes, the opportunity to study the Markov processes in detail. Besides, the objective is to provide the students with knowledge about making inference on Markov processes, defining renewal processes and Brownian motion.

Learning Outcomes of the Course Unit

1   Making inferences on Markov processes
2   Defining characteristics of renewal processes
3   Performing calculations related with renewal processes
4   Appling Markov processes in various areas
5   Reviewing recent literature and present examples

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Branching process, definition, examples
2 Higher order Markov chains, reverse Markov chains
3 Statistical inference for Markov chains, estimation of transition probability matrix, hypothesis testing
4 Statistical inference for simple Markov processes, estimation of parameters, hypothesis testing
5 Renewal processes
6 Delayed renewal processes
7 Reward renewal processes
8 MIDTERM
9 Markov renewal process, semi-Markov process, regenerative process, Presentation
10 Martingals, Azuma inequality, stopping times, Presentation
11 Random walk
12 Using Martingals to analyze random walk, Homework
13 Brownian motion and other Markov processes, Homework
14 Brownian motion and other Markov processes

Recomended or Required Reading

Textbook(s):
U. N. Bhat, G.K. Miller, 2002, Elements of Applied Stochastic Processes, Wiley Series in Probability and Statistics, New Jersey.

References:
S. M. Ross, 1996, Stochastic Processes, Wiley Series in Probability and Statistics, New Jersey.
S.M. Ross, 1970, Applied Probability Models with Optimization Applications, Dover Publications, New York.

Materials: None

Planned Learning Activities and Teaching Methods

Lecture, problem solving, homework, presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 PRS PRESENTATION
3 FCG FINAL COURSE GRADE ASG * 0.50 + PRS * 0.50


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
Preparation for midterm exam 1 10 10
Preparation for final exam 1 15 15
Preparing assignments 2 20 40
Preparing presentations 2 20 40
Preparations before/after weekly lectures 14 4 56
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 207

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1545
LO.25455
LO.3555
LO.454555
LO.554454454

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

Copyright 2015 DEÜ. BİD

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