"Strong approximations of three-dimensional Wiener sausages"

Endre Csáki and Yueyun Hu

Summary: 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.

Keywords: Wiener sausage, intersection local times, strong approximation.

AMS 2000 subject classification: 60F15.