Strong approximations of three-dimensional Wiener sausages

Details Strong approximations of three-dimensional Wiener sausages Strong approximations of three-dimensional Wiener sausages

2004-05-21

arxiv.org/abs/math/0405413v1

Mathematics

Probability

18 pages

Scientific paper

In this paper we prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall's estimates between the Wiener sausage and the Brownian intersection local times.

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