Introduction to Probability Theory and Stochastic Processes

Fall 2008, PSTAT 213A

Tu-Th 9:30-10:45 - GIRV 1115

Jean-Pierre Fouque

		
Office Hours: Fridays 10:30--12:30 or by appointment

		
		Office: South Hall 5504
		Phone:  893-5637
		fouque at pstat.ucsb.edu


TA: Matt Lorig, lorig@pstat.ucsb.edu

Discussion Time and Location: W 12:00-12:50; Girv 2124
Office hours: Tuesday 8:15-9:15 and 11:00-12:00; South Hall 5431T

Agenda:

Midterm exams: October 23 and November 20 (tentative)

Final exam: December 10 (8-11AM)

Week 1:

  • Thursday September 25: Random variables and more...

    Week 2:

  • September 30: Generating functions (5.1)
  • October 2: Generating functions (continued). Matching problem, Poisson distribution (5.2).

    Week 3:

  • October 7: Random Walk (5.3) Homework 1 Due: HW1
  • October 9: 5.3 continued. Branching processes (5.4).

    Week 4:

  • October 14: Branching processes (5.4). Homework 2 Due: 1, 6 p.155; 5, 8 p.162; 2 p.170; 3 p.206
  • October 16: Section 5.6.

    Week 5:

  • October 21: Characteristic functions (5.7 and 5.8). Homework 3 Due: 3 p.175; 11 p.207; 21 p.208
  • October 23: MIDTERM 1 (Chapter 5 sections 1-4, no documents)

    Week 6:

  • October 28: Limit Theorems (5.10). Homework 4 Due: 1, 5 p.181; 9 p.188
  • October 30: Large deviations (5.11).

    Week 7:

  • November 4: Markov Chains (6.1). Homework 5 Due: 4 p.206; 32, 33, 37 p.210
  • November 6: Classification (6.2-3).

    Week 8:

  • November 11: HOLIDAY
  • November 13: Sections 6.4 and 6.6. Homework 6 Due: 3, 6 p. 219; 1, 3 p.225-226.

    Week 9:

  • November 18: Review class given by Brian Wignall
  • November 20: MIDTERM 2 (Chapter 5 sections 6-8, 10, Chapter 6 sections 1-4, 6, no documents)

    Week 10:

  • November 25: Class given by Matt Lorig
  • November 27: HOLIDAY

    Week 11:

  • December 2: Poisson Process.
  • December 4: Examples in Queueing Theory.

    Course Outline

    The goal of the PSTAT 213ABC series is to give a rigorous introduction to probability and random processes. The combination of PSTAT 213ABC and PSTAT 210 is designed for those requiring a thorough understanding of basic probability theory and is thus aimed at students who plan to do research in statistics, applied probability, mathematical finance, economics, biology, computer science, or engineering. PSTAT 213A gives an introduction to Markov Chains and related processes without the use of measure theory. We will be emphasizing major ideas and techniques with long proofs sometimes being presented in outline.

    Material for this quarter will include:

  • Generating functions
  • Discrete time Markov chains, random walks and branching processes
  • Continuous time Markov chains; birth-death processes, queues
  • The Poisson Process and Point Processes (as time permits)

    Prerequisites: Introductory course on probability and statistics (PSTAT120AB or equivalent). A knowledge of basic measure theory (the theory of Lebesgue integration in particular) is required for PSTAT 213BC, but not PSTAT 213A. Students who lack such a background are advised to either enroll in PSTAT 210 (can be taken concurrently with PSTAT 213A) or to complete MATH 118ABC and MATH 201ABC (or equivalent). Analysis background is helpful but not necessary for PSTAT 213A.

    Grading: Homework 30%, Midterms(2) 40%, Final 30%

    TEXT:
    Grimmett-Stirzaker, Probability and Random Processes. Oxford University Press, Third Edition (2001).