office: MSB M222
office hours:   TTH 10:45-12:15
Courant Lecture Notes in Mathematics, 7. AMS 2001.
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.