Probability Theory: Math 605
Meeting : TuTh 1:002:15 LGRT 177
Instructor : Luc ReyBellet
Office : 1423 K LGRT
Phone : 5456020
EMail : luc@math.umass.edu
Office Hours : Tu 3:004:00, Th 9:3011:00, or by appointment
Text: The official text book for the class is

Probability and Stochastics by Erhan Cinlar. Graduate Texts in Mathematics 261.
Springer 2011
ISSN: 00725285 ISBN: 9780387878591. DOI:101007/9780387878591
This books makes a very good job introducing the main ideas of probability without getting lost in
too much technical details. m
Other very useful references:

Probability Essentials by Jean Jacod and Philip Protter, 2n edition. Universitext. Springer 2004.
ISBN: 9783540438717

A first look at rigorous probability by Jeffrey Rosenthal, 2n edition. World Scientific 2006
ISBN10: 9812703713 ISBN13: 9789812703712

A Probability Path by Sidney Resnick. Birkhauser 2014

Probability: Theory and Examples by Rick Durrett, 4th edition. Cambridge University Press ISBN10: 0521765390 ISBN13: 9780521765398

Real Analysis and Probability by R.M Dudley, 2nd edition. Cambridge University Press 2004

Probability by A. Shiryaev, 2nd edition. Springer 1995
Syllabus:
This is the first part of a 2semester introduction to probability (Semester 1) and stochastic process
(Semester 2). The prerequisites for this class is a good working knowledge of undergraduate
Probability (without measure theory), such as Stat 515 or STAT 607. Also required are some
mathematical maturity and familiarity with mathematical reasoning and of curse a fearless
adventurous spirit!
During the first semester we will cover some of the foundations of probability

1) Axioms of probability and the construction of probability spaces.

2) Random variable, integration, and convergence of random variable and the law of large numbers.

3) Gaussian random variables, characteristic and moment generation functions, the central limit theorem and concentration inequalities.

4) Conditional expectation, the radonnikodym theorem and martingales.
In the second semester we will study stochastic process, Poisson processes, Markov processes, Branching process, Renewal processes, and Brownian motion.
Grade: There will be a midterm exam and a final exam.
Homework will be assigned weekly. Each of the midterm, final and the combined homework will
be worth 1/3 of your grade.
Exams:
 Midterm: TBA Room: TBA
 Final: TBA
Homework :
Homework #1 (due on Friday September 13):
Set #1
Homework #2 (due on Friday September 20):
Set #2