APM 504 – Applied Probability and Stochastic Processes
Spring 2011

Instructor: Dr. Jay Taylor, office: PSA 447; phone: 965-2641; e-mail: jtaylor@math.asu.edu
Time: Mondays and Wednesdays 2:00-3:15
Location: PSA 104
Office Hours: Mondays 11:00-12:30 or by appointment.
Text: Probability: Theory and Examples (3rd Edition) by Rick Durrett

Course Description: This course will provide a rigorous, measure-theory based introduction to probability. Topics covered will include the weak and strong laws of large numbers, the central limit theorem, Poisson approximation, random walks and renewal theory, conditional expectations, and discrete parameter martingales. Although we won't spend much time discussing stochastic processes or models, we will cover the basic material needed to read and apply this part of the literature.

Problem Sets: Like most mathematical subjects, probability theory is best learned by solving problems. With this in mind, exercises will be assigned regularly and posted at the following link. Solutions will be posted at this same link a few days after each set is collected.

Final Exam: The final exam can be downloaded from the problem sets page and is due by 2:00 pm on 9 May.

Grading: Grades will be based on the problem sets (collectively worth 200 points) and on a take-home final exam (100 points) that will be distributed during the last week of class.

Syllabus: The following schedule is tentative. Please read the indicated sections in Durrett (2005).


Date

Topic

Sections in Durrett

19 Jan

Overview; Basic Definitions

1.1; A.1-A.3

24 Jan

Review of Lebesgue Integration

A.4-A.5

26 Jan

Random Variables; Expected Values

1.2-1.3

31 Jan

Independence

1.4

2 Feb

Weak Laws of Large Numbers

1.5

7 Feb

Borel-Cantelli Lemmas

1.6

9 Feb

Strong Law of Large Numbers

1.7

14 Feb

Convergence of Random Series

1.8

16 Feb

Large Deviations

1.9

21 Feb

De Moivre-Laplace Theorem

2.1

23 Feb

Weak Convergence

2.2

28 Feb

Weak Convergence

2.2

2 March

Characteristic Functions

2.3

7 March

Characteristic Functions

2.3

9 March

Central Limit Theorems

2.4

14 March

Spring Break


16 March

Spring Break


21 March

Poisson Approximation

2.6

23 March

Poisson Process

2.6

28 March

Exchangeability

3.1

30 March

Stopping Times

3.1

4 April

Recurrence

3.2

6 April

Recurrence

3.2

11 April

Conditional Expectations

4.1

13 April

Conditional Expectations

4.1

18 April

Martingales: Properties

4.2

20 April

Martingales: Limits

4.2

25 April

Martingales: Examples

4.3

27 April

Uniform Integrability

4.5

2 May

Optional Stopping Theorem

4.7