Moderate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages

Strong approximations of three-dimensional Wiener sausages

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 [10]’s fine L-norm estimates betwee...

Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks

We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times

Moderate Deviations and Law of the Iterated Logarithm for Intersections of the Ranges of Random Walks1 By

Moderate Deviations and Laws of the Iterated Logarithm for the Local times of Additive Lévy Processes and Additive Random Walks

We study the upper tail behaviors of the local times of the additive Lévy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L2-norms of the local times and for the local times at a fixed site. Subject classifications: 60F10, 60F15, 60J55, 60G52

Precise asymptotics in laws of the iterated logarithm for Wiener local time

In this paper, we study the asymptotic properties of the upper and lower tail probabilities of the maximum local time L∗(t) of Wiener process (Brownian motion), and obtain some precise asymptotics in the law of the iterated logarithm and the Chungs-type laws of the iterated logarithm for the supremum of Wiener local time L(x; t); x∈R; t ∈R+. c © 2003 Elsevier B.V. All rights reserved. MSC: 60F1...