An elementary approach to Brownian local time based on simple, symmetric random walks

Details An elementary approach to Brownian local time based on simple, symmetric random walks An elementary approach to Brownian local time based on simple, symmetric random walks

2010-08-10

arxiv.org/abs/1008.1701v1

Periodica Mathematica Hungarica, Volume 51, Number 1, Pages 79-98, (2005)

Mathematics

Probability

17 pages

Scientific paper

10.1007/s10998-005-0022-8

In this paper we define Brownian local time as the almost sure limit of the
local times of a nested sequence of simple, symmetric random walks. The limit
is jointly continuous in $(t,x)$. The rate of convergence is $n^{\frac14} (\log
n)^{\frac34}$ that is close to the best possible. The tools we apply are almost
exclusively from elementary probability theory.

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