Random walk local time approximated by a Wiener sheet combined with an independent Brownian motion

Details Random walk local time approximated by a Wiener sheet combined with an independent Brownian motion Random walk local time approximated by a Wiener sheet combined with an independent Brownian motion

2007-09-04

arxiv.org/abs/0709.0389v1

Mathematics

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Scientific paper

Let $\xi(k,n)$ be the local time of a simple symmetric random walk on the
line. We give a strong approximation of the centered local time process
$\xi(k,n)-\xi(0,n)$ in terms of a Wiener sheet and an independent Wiener
process, time changed by an independent Brownian local time. Some related
results and consequences are also established.

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