office hours: TTH 10:45-12:15
email: teplyaev
math.uconn.edu
http://www.math.uconn.edu/~teplyaev
office: MSB M222
office hours: TTH 10:45-12:15
email:
teplyaevmath.uconn.edu
http://www.math.uconn.edu/~teplyaev
| Textbook |
|---|
S.R.S. Varadhan
Probability theory
Courant Lecture Notes in Mathematics, 7.
AMS 2001.
| Course Outline |
|---|
This course is the first part of the one year graduate course in probability theory. The course requires a basic understanding of measure theory, but a short overview will be given in the first few lectures. An extra tutorial can be given if needed. The course will include: characteristic functions; convergence of random variables and probability measures; sums of independent random variables, including laws of large numbers, central limit theorems, convergence of series, distribution and moment inequalities, and possibly also large deviations and/or law of the iterated logarithm; conditional expectations and martingale theory, and other topics. Construction of the Brownian motion, continuous time martingales and stochastic integration will be included in Math 323, Spring 2004.