APM 504 –
Applied Probability and Stochastic Processes
Spring
2011
Instructor: Dr. Jay Taylor, office: PSA 447; phone:
9652641; email: jtaylor@math.asu.edu
Time: Mondays and Wednesdays 2:003:15
Location:
PSA 104
Office Hours: Mondays 11:0012:30 or by
appointment.
Text: Probability:
Theory and Examples (3^{rd} Edition) by Rick
Durrett
Course Description: This course will provide a rigorous, measuretheory 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 takehome 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.1A.3 
24 Jan 
Review of Lebesgue Integration 
A.4A.5 
26 Jan 
Random Variables; Expected Values 
1.21.3 
31 Jan 
Independence 
1.4 
2 Feb 
Weak Laws of Large Numbers 
1.5 
7 Feb 
BorelCantelli 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 MoivreLaplace 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 