280 Lecture Notes
Math 280C -- Probability Theory (Srping 2010) Course
- Homework #8 is being postponed until Wednesday June 2.
- The current plan is to have an extra class from 1-3 or so
on Friday June 4, 2010.
Driver, APM 5260, 534-2648
Office Hours: Monday and
Friday, 9:00 -- 11:00 AM
(Mike) Gao, APM 6422
Office Hours: Monday
and Tuesday, 4:00 -- 5:00 PM.
MWF 8:00 --
8:50 AM in APM 5402
Resnick, S. A Probability Path, Birkhauser, 1999.
Homework: There will be weekly
homework assignments due at the start of class on
Wednesday. No late homeworks will be accepted.
Description: Math 280ABC is the fundamental graduate
probability sequence. It covers measure theoretic probability essential for the
pursuit of research in probability or in fields in which probability is used in
applications. Topics to be covered include:
Measure and integration from a probabilistic perspective.
Basic probabilistic notions of random variables, expectation,
Limit theorems: laws of large numbers, convergence in
distribution, central limit theorems.
Martingale theory: conditional expectation, convergence
theorems, optional stopping.
Stochastic processes: a selection from random walk, Markov
chains, Brownian motion, Markov processes, statistical mechanics, stable
processes, stochastic integration.
Topics 1, 2, and parts of 3 will be covered in Math 280A. The remainder of topic
3, and topics 4 and 5 will be covered in the subsequent two quarters of Math
280B, C. The text below will be supplemented with class lecture notes.
Reserved Books: The following books have been put on
reserve at the Science and Engineering Library.
1. Author Resnick, Sidney I
Title A probability path / Sidney I. Resnick
Published Boston : Birkhäuser, c1999
2. Author Billingsley, Patrick
Title Probability and measure / Patrick Billingsley
Published New York : Wiley, c1986
Edition 2nd ed
3. Author Durrett, Richard, 1951-
Title Probability : theory and examples / Richard Durrett
Published Belmont, CA : Thomson, Brooks/Cole, c2005
Edition 3rd ed