UC Davis Math 235B
Probability Theory

Basic information

CRN code: 60748 (MAT 235 B) and 72574 (STA 235 B)
Room/Time: TR 10:30-11:50 am in Math Sci Building 1147
Instructor: Alexander Soshnikov
Office: Math Sci Building 3140
Office Hours: MW 11:00-11:50am , plus by appointment
E-mail: soshniko@math.ucdavis.edu
 
Midterm (take home): due February 13 by 10:30a.m. in class
Final (take home): due TBA by
Grading: Midterm 50%, Final Exam 50%
Webpage: www.math.ucdavis.edu/~soshniko/235b
 

Topical Outline

  • Conditional Expectation

  • Martingales

  • Markov Chains

  • Ergodic Theory

    • Textbook:

  • Probability: Theory and Examples (fourth edition) by Rick Durrett

    • Recommended reading:

  • Dan Romik's Lecture Notes for MAT235B, Winter 2011

  • Probability with Martingales by David Williams. Cambridge University Press, 1991.

  • An Introduction to Probability Theory and Its Applications, Vols. 1-2, by William Feller.

    • Lectures

    Lecture 1 (January 9): Introduction.

    Lecture 2 (January 11): Conditional Expectation (section 5.1).

    Lecture 3 (January 16): Conditional Expectation (section 5.1).

    Lecture 4 (January 18): Martingales (section 5.2).

    Lecture 5 (January 23): Martingales. Properties (section 5.2). Examples (section 5.3).

    Lecture 6 (January 25): Branching Processes (section 5.3.4).

    Lecture 7 (January 30): Upcrossing Inequality. Almost Sure Convergence. Doob's decomposition. (section 5.2).

    Lecture 8 (February 1): L^p Spaces. Convergence in L^p (section 5.4).

    Lecture 9 (February 6): Doob's Inequality. Convergence in L^P (section 5.4).
    Lecture 10 (February 8): Uniform Integrability. Convergence in L^1. (section 5.5) Branching Processes (section 5.3.4).
    Lecture 11 (February 13): Square Integrable Martingales (section 5.4.1)
    Lecture 12 (February 15): Markov Chains. Introduction.
    Lecture 13 (February 20): Markov Chains (sections 6.1 and 6.2)
    Lecture 14 (February 22): Extensions of the Markov Property (section 6.3).
    Lecture 15 (February 27): Strong Markov Property. Reflection Principle (section 6.3).
    Lecture 16 (March 1): Recurrence and Transience (section 6.4).
    Lecture 17 (March 6): Recurrence and Transience (section 6.4).
    Lecture 18 (March 8): Recurrence and Transience (section 6.4).
    Lecture 19 (March 13): Stationary Measures (section 6.5).
    Lecture 20 (March 15): Stationary Measures (section 6.5).

    Homework, Midterm, and Final Exam.

    Homework will be posted online each Thursday.

    Midterm is due in class on Thursday, February 11 at 03:10p.m.

    Final Exam is due on Tuesday, March 20 at 03:00p.m.

    Homework 1

    (assigned on January 18):
    Homework 1 (pdf file)

    Homework 2

    (assigned on January 29):
    Homework 2 (pdf file)

    Midterm Exam

    First Part of the Midterm (pdf file)

    Second Part of the Midterm (pdf file)

    Homework 3

    (assigned on February 20):
    Homework 3 (pdf file)

    Homework 4

    (assigned on March 1):
    Homework 4 (pdf file)

    Homework 5

    (assigned on March 8):
    Homework 5 (pdf file)

    Final Exam (due on Tuesday, 03/20/2018 at 3 p.m.)

    Final Exam (pdf file)