ISM 207

Spring 2010
Random Process Models in Engineering

 

 

Announcements:

           The midterm exam will be on Tuesday 5/11, and not on 5/4 as originally scheduled.

          

           All lectures (except for lecture 1) are recorded and available at http://webcast.ucsc.edu

           Lecture 1 is available at Lecture 1 video

 

Lectures:

           Tuesday and Thursdays, 12:00 – 1:45

            Room: JB 156

 

          

          

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 ISM 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:                2-3 pm Tuesdays and Thursdays

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

3/30

Linear Algebra and Probability Review

Probability Space

Independence

Cond Probability, Bayes Rule

Expectation and Cond. Expectation

Lecture 1 video

Durrett Chapter 1, pp 1-25 (Required)

Probability Notes Sections 2-6 (Reference)

 

 

 

2

4/1

Linear Algebra and Probability Review

Range, rank, etc.

Matrix Inverse

Matrix Diagonalization, Jordan Form

Singular Value Decomposition

Linear Algebra Notes

Assignment 1 out

3

4/6

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

4/8

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

5

4/13

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

4/15

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

4/20

Discrete Time Markov Chains

Definition and Examples

Transition Probabilities

Classification of States

Durrett Chapter 1, pp 28-48

Assignment 2 due

8

4/22

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

4/27

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

4/29

Discrete Time Markov Chains

Limit Theorems

Durrett Chapter1, pp 100-120

Assignment 5 out

11

5/4

Martingales

Conditional Expectation

Examples

Optional Stopping Theorem

Applications in Investing

 

Assignment 4 due

12

5/6

Martingales

Conditional Expectation

Examples

Optional Stopping Theorem

Applications in Investing

Durrett Chapter 2

 

13

5/11

MIDTERM

Durrett Chapter 2

Assignment 6 out

14

5/13

Poisson Processes

Exponential Distribution

Poisson process definition

Conditioning

Applications in Traffic Modeling

Durrett Chapter 3

Assignment 5 due

15

5/18

Continuous Time Markov Chains

Definitions and Examples

Transition Probabilities

Limit Behavior

Durrett Chapter 4

Assignment 7 out

16

5/20

Continuous Time Markov Chains

Reversibility

Queuing Networks

Call Center Models

Durrett Chapter 4

Assignment 6 due

17

5/25

Renewal Processes

Definitions

Laws of Large Numbers

Durrett Chapter 5, pp 209-221

Assignment 8 out

18

5/27

Renewal Processes

Queuing Applications

M/G/1 queue

Durrett Chapter 5, pp 221-234

Assignment 7 due

19

6/1

Brownian Motion

Definitions

Markov Property; Reflection Principle

 

Durrett Chapter 6

Assignment 8 due

20

6/3

Brownian Motion

Hitting Times

Black-Scholes

 

 

 

 

FINAL EXAM

June 9

8-11 am