"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
AMS 2000 subject classification: 60F15.