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

TL;DR

This paper characterizes the limiting distributions of a family of functionals related to the law of the iterated logarithm for Brownian motion on compact manifolds, using a functional analytic approach.

Contribution

It provides a complete characterization of the limiting distributions for the law of the iterated logarithm in the context of Brownian motion on compact manifolds.

Findings

Complete description of limiting distributions for the law of the iterated logarithm

Functional analytic framework applied to stochastic processes on manifolds

Advances understanding of asymptotic behavior of Brownian motion

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 $\{\mu_t, t>0\}$.