Some Measure-Valued Markov Processes Attached to Occupation Times of Brownian Motion

Abstract

We study the positive random measure Π t (ω,dy)=l t B t -ydy , where ( l t a;a∈R,t>0) denotes the family of local times of the one-dimensional Brownian motion B. We prove that the measure-valued process ( Π t;t≥0) is a Markov process. We give two examples of functions ( f i) i =1,...,n for which the process ( Π t(f i) i =1,...,n;t≥0) is a Markov process.