TIM 207

Spring 2012
Random Process Models in Engineering

Announcements:


Lectures:

Tuesday and Thursdays, 4:00 – 5:45

Room: JB 156  (Telecast to SVC)

Course Description:

TIM 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 TIM 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:                     1-2 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

Class #	Date	Topics	Reading	Assignments
1	4/3	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	4/5	Linear Algebra and Probability Review Range, rank, etc. Matrix Inverse Matrix Diagonalization, Jordan Form Singular Value Decomposition	Linear Algebra Notes	Assignment 1 Out
3	4/10	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	4/12	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
5	4/17	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	4/19	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	4/24	Discrete Time Markov Chains Definition and Examples Transition Probabilities Classification of States	Durrett Chapter 1, pp 28-48	Assignment 2 Due
8	4/26	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	5/1	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	5/3	Discrete Time Markov Chains Limit Theorems	Durrett Chapter1, pp 100-120	Assignment 5 out
11	5/8	Martingales Conditional Expectation Examples Optional Stopping Theorem Applications in Investing	Durrett Chapter 2	Assignment 4 due
12	5/10	MIDTERM Study Questions
13	5/15	Martingales Conditional Expectation Examples Optional Stopping Theorem Applications in Investing	Durrett Chapter 2	Assignment 5 due Assignment 6 out
14	5/17	Poisson Processes Exponential Distribution Poisson process definition Conditioning Applications in Traffic Modeling	Durrett Chapter 3
15	5/22	Continuous Time Markov Chains Definitions and Examples Transition Probabilities Limit Behavior	Durrett Chapter 4
16	5/24	Continuous Time Markov Chains Reversibility Queuing Networks Call Center Models	Durrett Chapter 4
17	5/29	Renewal Processes Definitions Laws of Large Numbers	Durrett Chapter 5, pp 209-221	Assignment 6 due Assignment 7 out
18	5/31	Renewal Processes Queuing Applications M/G/1 queue	Durrett Chapter 5, pp 221-234
19	6/5	Brownian Motion Definitions Markov Property; Reflection Principle	Durrett Chapter 6	Assignment 7 Due
20	6/7	Brownian Motion Hitting Times Black-Scholes
		FINAL EXAM June 11 4 - 7pm