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, 1011:45 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: 12pm 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 

Assignments 
1 
1/5 
Linear Algebra and Probability Review
Probability
Space
Cond
Probability, Bayes Rule
Expectation and
Cond. Expectaton 
Durrett Chapter 1, pp 125 (Required) Probability
Notes Sections 26 (Reference) 

2 
1/10 
Linear Algebra and Probability Review
Range, rank,
etc.
Matrix Inverse
Matrix
Diagonalization, Jordan Form
Singular Value
Decomposition 

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 212215 

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 215219 

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 219223 

7 
1/26 
Discrete Time Markov Chains
Definition and
Examples
Transition Probabilities
Classification
of States 
Durrett Chapter 1, pp 2848 

8 
1/31 
Discrete Time Markov Chains
Limit Behavior
Convergence
Theorems
Invariant
Distribution 
Durrett Chapter 1, pp 4865 

9 
2/2 
Discrete Time Markov Chains
Random Walk
First Passage
times
Queuing
Applications 
Durrett Chapter 1, pp 6688 
Hwk_3_Solutions 
10 
2/7 
Discrete Time Markov Chains
Strong Law for
Markov Chains
One step
calculations
Examples 


11 
2/9 
Discrete Time Markov Chains
Limit Theorems 
Durrett Chapter1, pp
100120 

12 
2/14 
MIDTERM 


13 
2/16 
Martingales
Conditional
Expectation
Examples
Optional
Stopping Theorem
Applications in
Investing 
Durrett Chapter 2 

14 
2/21 
Martingales
Conditional
Expectation
Examples
Optional
Stopping Theorem
Applications in
Investing 
Durrett Chapter 2 

15 
2/23 
Poisson Processes
Exponential
Distribution
Poisson process
definition
Conditioning
Applications in
Traffic Modeling 
Durrett Chapter 3 

16 
2/28 
Continuous Time Markov Chains
Definitions and
Examples
Transition
Probabilities
Limit Behavior 
Durrett Chapter 4 

17 
3/2 
Continuous Time Markov Chains
Reversibility
Queuing
Networks

Durrett Chapter 4 

18 
3/7 
Renewal Processes
Definitions
Laws of Large
Numbers 
Durrett Chapter 5, pp
209221 
(Corrected) 
19 
3/9 
Renewal Processes
Queuing
Applications
M/G/1 queue 
Durrett Chapter 5, pp
221234 

20 
3/14 
Brownian Motion
Definitions
Markov Property;
Reflection Principle
Hitting Times 
Durrett Chapter 6, pp
242257 

21 
3/16 
Brownian Motion Applications
Option pricing
in discrete time
BlackScholes 
Durrett Chapter 6, pp
257264 
(Corrected) 

3/22 811am 
FINAL EXAM In JB 169 

* See announcement above