On the law of the iterated logarithm for Brownian motion on compact manifolds

Abstract

By taking a functional analytic point of view, we consider a family of distributions (continuous linear functionals on smooth functions), denoted by $\{{\mu }_t,t>0\}$, associated to the law of iterated logarithm for Brownian motion on a compact manifold. We give a complete characterization of the collection of limiting distributions of $\{{\mu }_t,t>0\}$.