Local time of Martin-Lof Brownian motion

Abstract

In this paper we study the local times of Brownian motion from the point of view of algorithmic randomness. We introduce the notion of effective local time and show that any path which is Martin-L\"of random with respect to the Wiener measure has continuous effective local times at every computable point. Finally we obtain a new simple representation of classical Brownian local times, computationally expressed.