Quasi sure local convergence rate of a Brownian motion in the Hölder norm

Abstract

We estimate the local convergence rate of Strassen type for a Brownian motion in the Hölder norm with respect to C r , p C_{r,p} -capacity on an abstract Wiener space. The local convergence rate for increments of a Brownian motion in the Hölder norm with respect to C r , p C_{r,p} -capacity is also derived.