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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.
Last modified:
March 29, 2004
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