ISM 207

Winter 2008
Random Process Models in Engineering

Website: http://www.soe.ucsc.edu/classes/ism207/Winter08/

 

Announcements:

·        Lecture 14 is moved from Thursday 2/21 to Wednesday 2/20 at 10am in room E2 486.

·        The midterm will now be on Tuesday Feb 19.

 

·        The earlier planned makeup lecture on Wednesday 1/30 was cancelled. We will now have a makeup lecture on Wednesday 2/6, at 10 am, in room 486, in the E2 building. See revised lecture plan below.

Lectures:

          Tuesday and Thursdays, 10-11:45 in room: Crown 105

          See map

          Course Number: 42446

 

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

       I will modify this plan after reviewing the surveys I distribute on the first day of class.

 

Class #

Date

Topics

Reading

 

Assignments

1

1/8

Linear Algebra and Probability Review

*  Probability Space

*  Independence

*  Cond Probability, Bayes Rule

*  Expectation and Cond. Expectation

*  [notes]

Durrett Chapter 1, pp 1-25 (Required)

Probability Notes Sections 2-6 (Reference)

 

 

 

2

1/10

Linear Algebra and Probability Review

*  Range, rank, etc.

*  Matrix Inverse

*  Matrix Diagonalization, Jordan Form

*  Singular Value Decomposition

*  [notes]

Linear Algebra Notes

Assignment 1 out

3

1/15

Gaussian Random Vectors

*  CLT background

*  Normal Distribution and Density

*  Covariance Matrix

*  Jointly Gaussian Concept

*  LLSE

*  [notes, lectures3-6]

·         Gallager Notes on Gaussian Random Vectors

·         Probability Notes Section 7

·         Gallager Estimation Notes (Reference)

·         Gallager Detection Notes (Reference)

 

 

4

1/17

Random Processes and Linear Systems

*  Random Process definition

*  White Noise

*  Linear Time Invariant systems

*  [notes, lectures3-6]

·         Gallager Notes on Stochastic Processes

      - (Section 1 and 2)

·         Probability Notes Section 13, pp 212-215

Assignment 2 Out

Assignment 2 Hints

5

1/22

Random Processes and Linear Systems

*  Discrete Fourier Transform

*  Wide Sense Stationarity

*  [notes, lectures3-6]

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

·         Probability Notes Section 13 pp 215-219

Assignment 1 due

6

1/24

Random Processes and Linear Systems

*  Power Spectrum

*  LTI systems driven by random processes

*  Wiener Filter Preview

*  [notes, lectures3-6]

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

·         Probability Notes Section 13 pp 219-223

Assignment 3 Out

7

1/29

Discrete Time Markov Chains

*  Definition and Examples

*  Transition Probabilities

*  Classification of States

*  [notes]

Durrett Chapter 1, pp 28-48

Assignment 2 Due

Assignment 2 Hints

1/31

1/30 (wed.)

10 am,

E2-486

PLANNED “MAKEUP” LECTURE CANCELLED DUE TO INSTRUCTOR BEING SICK.

 

8

2/5

Discrete Time Markov Chains

*  Limit Behavior

*  Convergence Theorems

*  Invariant Distribution

Durrett Chapter 1, pp 48-65

Assignment 3 Due

Assignment 4 Out

9

(MAKEUP

LECTURE)

2/6

(wed.)

10 am,

E2-486

Discrete Time Markov Chains

*  Random Walk

*  First Passage times

*  Queuing Applications

Durrett Chapter 1, pp 66-88

10

2/7

Discrete Time Markov Chains

*  Strong Law for Markov Chains

*  One step calculations

*  Examples

 

11

2/12

Discrete Time Markov Chains

*  Limit Theorems

Durrett Chapter1, pp 100-120

Assignment 4 Due

12

2/14

Martingales

*  Conditional Expectation

*  Examples

*  Optional Stopping Theorem

*  Applications in Investing

Durrett Chapter 2

Assignment 5 Out

13

2/19

MIDTERM

 

14

2/21

2/20

(wed.)

10 am,

E2-486

Martingales

*  Conditional Expectation

*  Examples

*  Optional Stopping Theorem

*  Applications in Investing

Durrett Chapter 2

15

2/26

Poisson Processes

*  Exponential Distribution

*  Poisson process definition

*  Conditioning

*  Applications in Traffic Modeling

Durrett Chapter 3

Assignment 6 Out

16

2/28

Continuous Time Markov Chains

*  Definitions and Examples

*  Transition Probabilities

*  Limit Behavior

Durrett Chapter 4

Assignment 5 Due

 

17

3/4

Continuous Time Markov Chains

*  Reversibility

*  Queuing Networks

*  Call Center Models

Durrett Chapter 4

18

3/6

Renewal Processes

*  Definitions

*  Laws of Large Numbers

Durrett Chapter 5, pp 209-221

Assignment 6 Due

Assignment 7 Out

19

3/11

Renewal Processes

*  Queuing Applications

*  M/G/1 queue

Durrett Chapter 5, pp 221-234

20

3/13

Brownian Motion

*  Definitions

*  Markov Property; Reflection Principle

*  Hitting Times

*  Black-Scholes

Durrett Chapter 6

Assignment 7 Due

Assignment 8 Out

3/21 (Friday)

 8-11 AM

FINAL EXAM

In Crown 105

Assignment 8 Due