We study the positive random measure , where denotes the family of local times of the one-dimensional Brownian motion B. We prove that the measure-valued process is a Markov process. We give two examples of functions for which the process is a Markov process.
"Some measure-valued Markov processes attached to occupation times of Brownian motion." Bernoulli 6 (1) 63 - 72, Feb 2000.