Small ball probabilities for a Wiener process under weighted sup-norms, with an application to the supremum of bessel local times

Abstract

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup0<1≦1(t −p R(t)) and sup t ≧0(e−1R(t)), withp∈[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.