ISM 207

Winter 2006
Random Process Models in Engineering

Website: http://www.soe.ucsc.edu/classes/ism207/Winter06/

 

Announcements:

Corrected solutions for homeworks 9 and 10 below.

           

Lectures:

          Tuesday and Thursdays, 10-11:45 in room: J. Baskin 169

          Course Number: 45035

 

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:              1-2pm 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

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

 

Class #

Date

Topics

Reading

 

Assignments

1

1/5

Linear Algebra and Probability Review

*       Probability Space

*       Independence

*       Cond Probability, Bayes Rule

*       Expectation and Cond. Expectaton

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

Linear Algebra Notes

Homework 1 out

Hwk1 hints

3

1/12

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

1/17

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

Homework 2 out

Hwk 2 Hints

5

1/19

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

Homework 1 due

Hwk 1 Hints

Hwk_1_Solutions

6

1/24

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

Homework 3 out

(updated 1-26-06)

7

1/26

Discrete Time Markov Chains

*       Definition and Examples

*       Transition Probabilities

*       Classification of States

Durrett Chapter 1, pp 28-48

Homework 2 due

Hwk 2 Hints

Hwk_2_Solutions

8

1/31

Discrete Time Markov Chains

*       Limit Behavior

*       Convergence Theorems

*       Invariant Distribution

Durrett Chapter 1, pp 48-65

Homework 4 out

Hwk 4 Hints

Hwk_4_Solutions

9

2/2

Discrete Time Markov Chains

*       Random Walk

*       First Passage times

*       Queuing Applications

Durrett Chapter 1, pp 66-88

Homework 3 due

(updated 1-26-06)

Hwk_3_Solutions

10

2/7

Discrete Time Markov Chains

*       Strong Law for Markov Chains

*       One step calculations

*       Examples

 

Homework 5 out

Hwk 5 Clarification

Hwk_5_Solutions

11

2/9

Discrete Time Markov Chains

*       Limit Theorems

Durrett Chapter1, pp 100-120

Homework 4 due

Hwk 4 Hints

Hwk_4_Solutions

12

2/14

MIDTERM

 

 

13

2/16

Martingales

*       Conditional Expectation

*       Examples

*       Optional Stopping Theorem

*       Applications in Investing

Durrett Chapter 2

Homework 5 due

Hwk 5 Clarification

Hwk_5_Solutions

Homework 6 out

Hwk 6 Solutions

14

2/21

Martingales

*       Conditional Expectation

*       Examples

*       Optional Stopping Theorem

*       Applications in Investing

Durrett Chapter 2

Homework_7 out

Hwk 7 Hints

Hwk 7 Solutions

15

2/23

Poisson Processes

*       Exponential Distribution

*       Poisson process definition

*       Conditioning

*       Applications in Traffic Modeling

Durrett Chapter 3

Homework 6 due

Hwk 6 Solutions

16

2/28

Continuous Time Markov Chains

*       Definitions and Examples

*       Transition Probabilities

*       Limit Behavior

Durrett Chapter 4

Homework 8 out

Hwk 8 Hints

Hwk 8 Solutions

17

3/2

Continuous Time Markov Chains

*       Reversibility

*       Queuing Networks

*       Call Center Models

Durrett Chapter 4

Homework 7 Due

Hwk 7 Hints

Hwk 7 Solutions

 

18

3/7

Renewal Processes

*       Definitions

*       Laws of Large Numbers

Durrett Chapter 5, pp 209-221

Homework 9 out

Hwk 9 Hints

Hwk 9 Solutions

(Corrected)

19

3/9

Renewal Processes

*       Queuing Applications

*       M/G/1 queue

Durrett Chapter 5, pp 221-234

Homework 8 due

Hwk 8 Hints

Hwk 8 Solutions

20

3/14

Brownian Motion

*       Definitions

*       Markov Property; Reflection Principle

*       Hitting Times

Durrett Chapter 6, pp 242-257

* Homework 10 out

 

Hwk 10 Solutions

21

3/16

Brownian Motion Applications

*       Option pricing in discrete time

*       Black-Scholes

Durrett Chapter 6, pp 257-264

Homework 9 due

Hwk 9 Hints

Hwk 9 Solutions

(Corrected)

 

3/22

8-11am

FINAL EXAM

In JB 169

 

* Homework 10 due

Hwk 10 Solutions

            * See announcement above