ISM 207

Winter 2007
Random Process Models in Engineering

Website: http://www.soe.ucsc.edu/classes/ism207/Winter07/

 

Announcements:

Graded Homework 7s are outside my door.

 

Homework 8 solutions are also outside my door. You should take one only after turning in your homework 8. You can leave homework 8 in the box by my door.

           

Lectures:

          Tuesday and Thursdays, 12-1:45 in room: J. Baskin 156

          Course Number: 43342

 

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

1/4

Linear Algebra and Probability Review

*       Probability Space

*       Independence

*       Cond Probability, Bayes Rule

*       Expectation and Cond. Expectaton

*       Lecture notes

Durrett Chapter 1, pp 1-25 (Required)

Probability Notes Sections 2-6 (Reference)

 

 

 

2

1/9

Linear Algebra and Probability Review

*       Range, rank, etc.

*       Matrix Inverse

*       Matrix Diagonalization, Jordan Form

*       Singular Value Decomposition

*       Lecture notes

Linear Algebra Notes

Homework 1 out

Hwk_1_Solutions

3

1/11

Gaussian Random Vectors

*       CLT background

*       Normal Distribution and Density

*       Covariance Matrix

*       Jointly Gaussian Concept

*       LLSE

*       Lecture notes

·         Gallager Notes on Gaussian Random Vectors

·         Probability Notes Section 7

·         Gallager Estimation Notes (Reference)

·         Gallager Detection Notes (Reference)

 

 

4

1/16

Random Processes and Linear Systems

*       Random Process definition

*       White Noise

*       Linear Time Invariant systems

*       Lecture notes

·         Gallager Notes on Stochastic Processes

      - (Section 1 and 2)

·         Probability Notes Section 13, pp 212-215

Homework 2 out

Homework 2 Hints

Hwk 2 Solutions

5

1/18

Random Processes and Linear Systems

*       Discrete Fourier Transform

*       Wide Sense Stationarity

*       Lecture notes

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

·         Probability Notes Section 13 pp 215-219

Homework 1 due

Hwk_1_Solutions

6

1/23

Random Processes and Linear Systems

*       Power Spectrum

*       LTI systems driven by random processes

*       Wiener Filter Preview

*       Lecture notes

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

·         Probability Notes Section 13 pp 219-223

Homework 3 out

7

1/25

Discrete Time Markov Chains

*       Definition and Examples

*       Transition Probabilities

*       Classification of States

*       Lecture notes

Durrett Chapter 1, pp 28-48

Homework 2 due

Homework 2 Hints

Hwk 2 Solutions

8

1/30

Discrete Time Markov Chains

*       Limit Behavior

*       Convergence Theorems

*       Invariant Distribution

*       Lecture notes

Durrett Chapter 1, pp 48-65

Homework 4 out

 

9

2/1

Discrete Time Markov Chains

*       Random Walk

*       First Passage times

*       Queuing Applications

*       Lecture notes

Durrett Chapter 1, pp 66-88

Homework 3 due

Hwk 3 Solutions

10

2/6

Discrete Time Markov Chains

*       Strong Law for Markov Chains

*       One step calculations

*       Examples

*       Lecture notes

 

Homework 5 out

11

2/8

Discrete Time Markov Chains

*       Limit Theorems

*       Lecture notes

Durrett Chapter1, pp 100-120

Homework 4 due

Hwk 4 Solutions

12

2/13

MIDTERM

 

 

13

2/15

Martingales

*       Conditional Expectation

*       Examples

*       Optional Stopping Theorem

*       Applications in Investing

*       Lecture notes

Durrett Chapter 2

 

14

2/20

Martingales

*       Conditional Expectation

*       Examples

*       Optional Stopping Theorem

*       Applications in Investing

*       Lecture_notes

Durrett Chapter 2

Homework 6 out

15

2/22

Poisson Processes

*       Exponential Distribution

*       Poisson process definition

*       Conditioning

*       Applications in Traffic Modeling

*       Lecture_notes

Durrett Chapter 3

Homework 5 due

Hwk 5 Solutions

16

2/27

Continuous Time Markov Chains

*       Definitions and Examples

*       Transition Probabilities

*       Limit Behavior

*       Lecture notes

Durrett Chapter 4

 

17

3/1

Continuous Time Markov Chains

*       Reversibility

*       Queuing Networks

*       Call Center Models

*       Lecture notes

Durrett Chapter 4

Homework 6 due

Homework 7 out

Hwk 6 Solutions

18

3/6

3/7

12:30-2:15

E2-280

Renewal Processes

*       Definitions

*       Laws of Large Numbers

*       Lecture notes

Durrett Chapter 5, pp 209-221

 

19

3/8

Renewal Processes

*       Queuing Applications

*       M/G/1 queue

*       Lecture notes

Durrett Chapter 5, pp 221-234

Homework 8 out

20

3/13

Brownian Motion

*       Definitions

*       Markov Property; Reflection Principle

*       Hitting Times

*       Lecture notes

Durrett Chapter 6, pp 242-257

Homework 7 due

Hwk 7 Solutions

21

3/15

Brownian Motion Applications

*       Option pricing in discrete time

*       Black-Scholes

*       Lecture notes

Durrett Chapter 6, pp 257-264

 

 

3/21

8-11am

FINAL EXAM

In JB 156

 

Homework 8 due