Some Estimates for Planar Random Walk and Brownian Motion

Details Some Estimates for Planar Random Walk and Brownian Motion Some Estimates for Planar Random Walk and Brownian Motion

2006-11-06

arxiv.org/abs/math/0611127v1

Mathematics

Probability

18 pages, 2 figures

Scientific paper

The purpose of this note is to collect in one place a few results about simple random walk and Brownian motion which are often useful. These include standard results such as Beurling estimates, large deviation estimates, and a method for coupling the two processes, as well as solutions to the discrete Dirichlet problem in various domains which, to the author's knowledge, have not been published anywhere. The main focus is on the two-dimensional processes.

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