Uniform oscillations of the local time of iterated Brownian motion

Abstract

Burdzy and Khoshnevisan in 1995, Csáki et al. in 1996 and Xiao in 1997 have given some interesting information about the modulus of continuity of the local time of iterated Brownian motion. The aim of this paper is to provide the exact rate functions, respectively for the modulus of continuity and for the modulus of non-differentiability. Our approach strongly relies on Ray-Knight theorems for Brownian local times and on fine properties of Bessel processes.