STOCHASTIC PROCESSES - Fall 1999

 

Professor: Dr. Betsy Greenberg
 
  Office: CBA 6.306
  Hours: MW 1:30-2:30
    or by appointment
  E-mail betsyg@mail.utexas.edu
  Phone: 471-1756
Teaching Assistant: Tatiana Encheva
 
  Office: ETC 5.110
  Hours: TuTh 12:30-1:30
    or by appointment
  E-mail taniae@mail.utexas.edu
Text: Sheldon M Ross, Introduction to Probability Models, 6th Edition, Academic Press, 1997.

Grade:

Homework      10%
Tests (2)          30% each
Final exam       30%
Brief Description:
This course offers an introduction to Stochastic Processes, concentrating on the areas of Poisson Processes, Markov Chains, and Renewal Theory. In addition to the theory, examples of applications to various stochastic systems -- such as queueing systems and inventory models are presented. We will be following the textbook in the following order: Chapter 2, 3, 5, 7, 4, and 6.

Students are assumed to be familiar with the material in Chapters 1 and 2 of the textbook. If you have a lot of difficulty with the first homework assignment, you should drop this course and add M362K (Probability). An introductory course covering both probability and statistics may not provide sufficient background in probability.

SYLLABUS
 
Week
Date
Topic
Reading
1
Aug 26
 Review of Probability
2.4 - 2.6
2
31
 
Sept 2
 Review of Probability 

Conditional Expectation
2.7-2.8
 
3.1-3.4
3
7
 
9
 Conditional Probability 

Applications
3.5
 
3.6
4
14
 
16
 Exponential Distribution 

Poisson Process
5.1, 5.2
 
5.3
5
21
 
23
 Generalizations 

Renewal Theory
5.4
 
7.1, 7.2
6
28
 
30
 Test # 1 

Limit Theorems
--
 
7.3
7
Oct 5
 
7
 Renewal Reward Processes 

Alternating Renewal Processes
7.4
 
7.5
8
12
 
14
 The Inspection Paradox 

The Renewal Function
7.7
 
7.8
9
19
 
21
 Markov Chains 

Classification of States
4.1, 4.2
 
4.3
10
26
 
28
 Limiting Probabilities 

Applications
4.4
 
4.5
11
Nov 2
 
4
 Branching Processes 

Time Reversability
4.6
 
4.7
12
9
 
11
 Semi-Markov Processes 

Test # 2
7.6
 
--
13
16
 
18
 Continuous Time Markov Chains 

Birth and Death Chains 
6.1, 6.2
 
6.3, 6.4
14
23
 
25
 Limiting Probabilities 

Thanksgiving
6.5
 
--
15
30
 
Dec 2
 Time Reversibility 

Review
6.6
 
--
 
10
 Friday, 9:00 – 12 noon  
 
 
HOMEWORK ASSIGNMENTS
 
Number
Due Date
Problems
1
 Tu - Sept 7 Ch 2: 20, 25, 30, 43, 63, 74 
Ch 3: 5, 12, 20, 35
2
 Th - Sept 16 Ch 3: 44, 60, 66, 73 
Ch 5: 1, 8, 11, 15, 18, 19
3
 Th - Sept 23 Ch 5: 29, 32, 33, 38, 42
3*
 Tu - Oct 5 Ch 5:  48, 49, 56, 63, 66
4
 Th - Oct 14 Ch 7: 1, 2, 4, 7, 9, 12, 14, 16, 18
5
 Th - Oct 21 Ch 7: 19, 20, 22, 24, 25, 28, 31, 33, 34
6
 Tu - Nov 2 Ch 4: 5, 8, 9, 13, 14, 16, 17
7
 Tu - Nov 9 Ch 4: 25, 33, 39, 49
8
 Th – Nov 18 Ch 4: 52, 57, 58 
Ch 7: 38 
Ch 6: 1, 3, 5
9
 Th - Dec 2 Ch 6: 6, 8, 12, 17, 20, 22, 23, 29, 31, 36