Some measure-valued Markov processes attached to occupation times of Brownian motion

We study the positive random measure Pi(t)(omega, dy) = l(t)(Bt-y) dy, wher e (l(t)(a); a is an element of R, t > 0) denotes the family of local times of the one-dimensional Brownian motion B. We prove that the measure-valued process (Pi(t); t greater than or equal to 0) is a Markov proces. We give t wo examples of functions (f(i))(i=1,...,n) for which the process (Pi(t)(f(i ))(i=1,...,n); t greater than or equal to 0) is a Markov process.