ISM 207

Fall 2008
Random Process Models in Engineering

Website: http://www.soe.ucsc.edu/classes/ism207/Fall08/

Announcements:

Midterm Sample Questions

Final Sample Questions

Lectures:

Tuesday and Thursdays, 12-1:45 in room: Porter 241

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, 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

Class #	Date	Topics	Reading	Assignments
1	9/25	Linear Algebra and Probability Review Probability Space Independence Cond Probability, Bayes Rule Expectation and Cond. Expectation	Durrett Chapter 1, pp 1-25 (Required) Probability Notes Sections 2-6 (Reference)
2	9/30	Linear Algebra and Probability Review Range, rank, etc. Matrix Inverse Matrix Diagonalization, Jordan Form Singular Value Decomposition	Linear Algebra Notes	Assignment 1 out
3	10/2	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	10/7	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 Assignment 2 Hint
5	10/9	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	10/14	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	10/16	Discrete Time Markov Chains Definition and Examples Transition Probabilities Classification of States	Durrett Chapter 1, pp 28-48	Assignment 2 due Assignment 2 Hint
8	10/21	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	10/23	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	10/28	Discrete Time Markov Chains Limit Theorems	Durrett Chapter1, pp 100-120
11	10/30	Martingales Conditional Expectation Examples Optional Stopping Theorem Applications in Investing	Durrett Chapter 2	Assignment 4 due [hint]
12	11/4	Martingales Conditional Expectation Examples Optional Stopping Theorem Applications in Investing	Durrett Chapter 2	Assignment 5 out
13	11/6	MIDTERM
	11/11	Veterans Day Holiday		Assignment 6 out
14	11/13	Poisson Processes Exponential Distribution Poisson process definition Conditioning Applications in Traffic Modeling	Durrett Chapter 3	Assignment 5 due
15	11/18	Continuous Time Markov Chains Definitions and Examples Transition Probabilities Limit Behavior	Durrett Chapter 4	Assignment 7 Out
16	11/20	Continuous Time Markov Chains Reversibility Queuing Networks Call Center Models	Durrett Chapter 4	Assignment 6 due [solutions]
17	11/25	Renewal Processes Definitions Laws of Large Numbers	Durrett Chapter 5, pp 209-221	Assignment 8out
	11/27	Thanksgiving Holiday
18	12/2	Renewal Processes Queuing Applications M/G/1 queue	Durrett Chapter 5, pp 221-234	Assignment 7 due [solutions]
19	12/4	Brownian Motion Definitions Markov Property; Reflection Principle Hitting Times Black-Scholes	Durrett Chapter 6	Assignment 8 due [solutions]
		FINAL EXAM Tuesday, 12/9, 8am-11am Porter 241 [sample questions]