TIM 207
Spring 2012
Random Process Models in
Engineering
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, 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
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 |
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 |
|
Assignment 4 due |
12 |
5/10 |
MIDTERM Study Questions |
|
|
13 |
5/15 |
Martingales
Conditional Expectation Examples Optional Stopping Theorem |
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 |
|