ISM 207

Fall 2008
Random Process Models in Engineering

Website: http://www.soe.ucsc.edu/classes/ism207/Fall08/

 

Announcements:

          Midterm Sample Questions

            Final Sample Questions

 

Lectures:

          Tuesday and Thursdays, 12-1:45 in room: Porter 241

 

Course Description:

ISTM 207 is a first graduate course in stochastic process modeling and analysis for applications in technology management, information systems design, and engineering. Many problems in technology management, information systems, and as well as engineering in general, involve decision making in an uncertain and dynamically changing environment. Stochastic process modeling is thus an essential topic for students in these fields. In ISTM 207, students will learn both the fundamental techniques of analyzing stochastic processes, as well as acquire a sense of how to identify the best techniques to study problems that arise in technology management, information systems, and engineering.

 

Instructor:

          John Musacchio (johnm@soe.ucsc.edu)

Office:                         E2 Room 557

Office hours:              TBA

Email:                         johnm@soe.ucsc.edu

 

Textbook

            ‘Essentials of Stochastic Processes’ by Rick Durrett, 1st ed., Springer (1999).

           

            Other reading materials may be distributed from the website in the “reading” column of the lecture plan chart.

 

Grading:

          Midterm               30%

          Homework           40%

          Final Exam                    30%

 

          Homework will be assigned approximately once per week throughout the quarter.

 

Tentative Lecture Plan

 

 

Class #

Date

Topics

Reading

 

Assignments

1

9/25

Linear Algebra and Probability Review

*  Probability Space

*  Independence

*  Cond Probability, Bayes Rule

*  Expectation and Cond. Expectation

Durrett Chapter 1, pp 1-25 (Required)

Probability Notes Sections 2-6 (Reference)

 

 

 

2

9/30

Linear Algebra and Probability Review

*  Range, rank, etc.

*  Matrix Inverse

*  Matrix Diagonalization, Jordan Form

*  Singular Value Decomposition

Linear Algebra Notes

Assignment 1 out

3

10/2

Gaussian Random Vectors

*  CLT background

*  Normal Distribution and Density

*  Covariance Matrix

*  Jointly Gaussian Concept

*  LLSE

·         Gallager Notes on Gaussian Random Vectors

·         Probability Notes Section 7

·         Gallager Estimation Notes (Reference)

·         Gallager Detection Notes (Reference)

 

 

4

10/7

Random Processes and Linear Systems

*  Random Process definition

*  White Noise

*  Linear Time Invariant systems

·         Gallager Notes on Stochastic Processes

      - (Section 1 and 2)

·         Probability Notes Section 13, pp 212-215

Assignment 2 out

Assignment 2 Hint

5

10/9

Random Processes and Linear Systems

*  Discrete Fourier Transform

*  Wide Sense Stationarity

·         Gallager Notes on Stochastic Processes   - (Section 2 and 5)

·         Probability Notes Section 13 pp 215-219

Assignment 1 due

6

10/14

Random Processes and Linear Systems

*  Power Spectrum

*  LTI systems driven by random processes

*  Wiener Filter Preview

·         Gallager Notes on Stochastic Processes - (White Gaussian Noise Section)

·         Probability Notes Section 13 pp 219-223

Assignment 3 out

7

10/16

Discrete Time Markov Chains

*  Definition and Examples

*  Transition Probabilities

*  Classification of States

Durrett Chapter 1, pp 28-48

Assignment 2 due

Assignment 2 Hint

8

10/21

Discrete Time Markov Chains

*  Limit Behavior

*  Convergence Theorems

*  Invariant Distribution

*  Random Walk

*  First Passage times

Durrett Chapter 1, pp 48-65

Assignment 4 out

9

10/23

Discrete Time Markov Chains

*  Queuing Applications

*  Strong Law for Markov Chains

*  One step calculations

*  Examples

Durrett Chapter 1, pp 66-88

Assignment 3 due

10

10/28

Discrete Time Markov Chains

*  Limit Theorems

Durrett Chapter1, pp 100-120

11

10/30

Martingales

*  Conditional Expectation

*  Examples

*  Optional Stopping Theorem

*  Applications in Investing

Durrett Chapter 2

Assignment 4 due

[hint]

12

11/4

Martingales

*  Conditional Expectation

*  Examples

*  Optional Stopping Theorem

*  Applications in Investing

Durrett Chapter 2

Assignment 5 out

13

11/6

MIDTERM

 

11/11

Veterans Day Holiday

Assignment 6 out

14

11/13

Poisson Processes

*  Exponential Distribution

*  Poisson process definition

*  Conditioning

*  Applications in Traffic Modeling

Durrett Chapter 3

Assignment 5 due

15

11/18

Continuous Time Markov Chains

*  Definitions and Examples

*  Transition Probabilities

*  Limit Behavior

Durrett Chapter 4

Assignment 7 Out

16

11/20

Continuous Time Markov Chains

*  Reversibility

*  Queuing Networks

*  Call Center Models

Durrett Chapter 4

Assignment 6 due

[solutions]

17

11/25

Renewal Processes

*  Definitions

*  Laws of Large Numbers

Durrett Chapter 5, pp 209-221

Assignment 8out

11/27

Thanksgiving Holiday

18

12/2

Renewal Processes

*  Queuing Applications

*  M/G/1 queue

Durrett Chapter 5, pp 221-234

Assignment 7 due

[solutions]

19

12/4

Brownian Motion

*  Definitions

*  Markov Property; Reflection Principle

*  Hitting Times

*  Black-Scholes

Durrett Chapter 6

Assignment 8 due

[solutions]

FINAL EXAM

Tuesday, 12/9, 8am-11am

Porter 241

[sample questions]