INDE599
SPECIAL TOPICS IN IE
Stochastic Processes
SPRING 2008
T Th 10:30-11:50 MEB 235
Instructor: Archis Ghate
Contact Information
Office: 141 D AERB
Office hours: Tuesdays 12:00-1:30
Email:archis@u.washington.edu
Phone: (206) 616-5968
Instructor’s webpage: http://web.mac.com/archis.ghate
Course webpage: http://courses.washington.edu/inde599s
Teaching Assistant : ChrisWang
Contact Information
Office: 106 MEB
Office hours: Tuesday, Thursday 4:00-5:30
Email:wangwei@u.washington.edu
Course Description:
A non-measure theoretic, yet rigorous introduction tostochasticprocesses for graduate students in engineering. Topics will includeconditionalexpectation, Poisson processes, renewal processes, Markov chains, Brownian motion etc.
Prerequisites:
An introductory course in probability covering named distributions, expected value etc and a course in calculus.
Textbook:
Stochastic Processes, by Sheldon M. Ross, Second Edition, WileySeriesin Probability and Mathematical Statistics, 1996.
Grading:
Homework 30%. We will have homework every week. One lowest homework grade will be dropped. Homework is due on Fridays no later than 5:00 pm.
Please put your homework in the TA mailbox assigned for this class on the ground floor of MEB.
Mid Term Exam 30%: The midterm will be a48hour take home exam roughly after 5 weeks of classes.
Final Exam 40%.: The final will be a 48 hour take home exam during finals week.
Approximate Course Outline
1. Introductiontostochastic processes.
a. Basicsofprobability.
b. Momentgenerating,characteristic functions.
c. Conditionalexpectation.
d. Exponentialdistribution,lack of memory.
e. Markovinequality,Chernoff bounds, limit theorems.
2. Poisson Processes
a. Definition
b. Inter-arrival andwaitingtime distributions.
c. Non-homogeneousandcompound Poisson processes.
3. Renewal Theory
a. Basic conceptsanddefinition
b. Key renewal theorem,Blackwell’stheorem, Wald’s equation.
c. Delayed andrewardrenewal processes.
4. Markov chains
a. Introduction,definitionand examples.
b. State classification.
c. Stationaryandlimiting distribution.
5. Continuous time Markovchains.
a. Introduction
6. Martingales andBrownianmotion (if time permits)
Reference Books:
Essentials of Stochastic Processes by Rick Durrett, Springer.
Adventures in Stochastic Processes by SidneyResnick,Birkhauser.
Course Policies:
You are allowed, in fact, encouraged to discuss homework problems in groups. However, the homework solutions must be written independently. You may not seek or provide inappropriate assistance to your fellow students during exams. This class is run according to the student conduct code available at http://www.washington.edu/students/handbook/conduct.html
Class Notes: Classnoteswill be posted weekly. Note that a majority of the material in the class notes below is taken from the textbook. Please do not reuse or distribute these notes without appropriate permissions.
Homework: all numbered problems are from the textbook.
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HW1 |
1.1, 1.8, 1.15, 1.18, 1.19, 1.25.
Suppose all moments of a random variable X are well-defined. Derive a relationship between its n th moment and the n th derivative of its characteristic function evaluated at u=0. |
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HW2 |
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HW3 |
2.7, 2.13, 2.26 |
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HW4 |
2.30, 2.32, 3.1, 3.2, 3.4, 3.7 |
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HW5 |
3.9, 3.11, 3.17, 3.21 |
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HW6 |
4.10, 4.12, 4.16, 4.31 |
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HW7
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