Cornell Math - MATH 671, Fall 2004

MATH 671: Probability—Martingales and Brownian Motion (Fall 2004)

Instructor: Gregory Lawler

Meeting Time & Room

This is the first course given by the Mathematics Department on measure-theoretic probability, but it will assume that the students have seen some of the material of OR&IE 651 or the equivalent. In particular, students should know measure theory (MATH 611 or 621 suffices for this) as well as the basic definitions of probability spaces, convergence (in probability, almost sure, in distribution), the weak and strong laws of large numbers, characteristic functions (i.e., Fourier transforms of probability measures), and the central limit theorem. Students with solid analysis backgrounds but missing the probability prerequisites should talk to me — the probability needed can be learned by some outside reading.

This course will cover martingales in discrete time, an introduction to random walk, and Brownian motion. (approximately 5,3,5 weeks, respectively).

The second semester course (MATH 672) will focus primarily on stochastic calculus and applications to partial differential equations.