ISM 207
Fall 2008
Random Process Models in Engineering
Website: http://www.soe.ucsc.edu/classes/ism207/Fall08/
Announcements:
Lectures:
Tuesday and Thursdays, 121:45 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 

Assignments 
1 
9/25 
Linear Algebra and Probability Review Probability Space Cond Probability, Bayes Rule Expectation and Cond. Expectation 
Durrett Chapter 1, pp 125 (Required) Probability
Notes Sections 26 (Reference) 

2 
9/30 
Linear Algebra and Probability Review Range, rank, etc. Matrix Inverse Matrix Diagonalization,
Jordan Form Singular Value Decomposition 

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 212215 

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 215219 

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 219223 

7 
10/16 
Discrete Time Markov Chains Definition and Examples Transition Probabilities Classification of States 
Durrett Chapter 1, pp 2848 

8 
10/21 
Discrete Time Markov Chains Limit Behavior Convergence Theorems Invariant Distribution Random Walk First Passage times 
Durrett Chapter 1, pp 4865 

9 
10/23 
Discrete Time Markov Chains Queuing Applications Strong Law for Markov Chains One step calculations Examples 
Durrett Chapter 1, pp 6688 

10 
10/28 
Discrete Time Markov Chains Limit Theorems 
Durrett Chapter1, pp 100120 

11 
10/30 
Martingales Conditional Expectation Examples Optional Stopping Theorem Applications in Investing 
Durrett Chapter 2 
[hint] 
12 
11/4 
Martingales Conditional Expectation Examples Optional Stopping Theorem Applications in Investing 
Durrett Chapter 2 

13 
11/6 
MIDTERM 


11/11 
Veterans Day Holiday 

14 
11/13 
Poisson Processes Exponential Distribution Poisson process definition Conditioning Applications in Traffic Modeling 
Durrett Chapter 3 

15 
11/18 
Continuous Time Markov Chains Definitions and Examples Transition Probabilities Limit Behavior 
Durrett Chapter 4 

16 
11/20 
Continuous Time Markov Chains Reversibility Queuing Networks Call Center Models 
Durrett Chapter 4 

17 
11/25 
Renewal Processes Definitions Laws of Large Numbers 
Durrett Chapter 5, pp 209221 

11/27 
Thanksgiving Holiday 

18 
12/2 
Renewal Processes Queuing Applications M/G/1 queue 
Durrett Chapter 5, pp 221234 

19 
12/4 
Brownian Motion Definitions Markov Property; Reflection Principle Hitting Times BlackScholes 
Durrett Chapter 6 

FINAL EXAM Tuesday,
12/9, 8am11am Porter 241 