A limit theorem for local time and application to random sets

For a broad class of Markov processes, we give a new intrinsic limit theorem for local time at a point x0x0. We suitably normalize the number of dyadic time boxes where the process passes through x0x0 before t>0t>0. We discuss the relation with other normalizations. We apply this result to the theory of random sets using tools from fractal theory. Our construction of the local time is well suited to Monte-Carlo simulations.