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, 1^st 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