A local limit theorem for densities of the additive component of a finite Markov Additive Process

摘要

In this paper, we are concerned with centered Markov Additive Processes {(Xt,Yt)}t∈T where the driving Markov process {Xt}t∈T has a finite state space. Under suitable conditions, we provide a local limit theorem for the density of the absolutely continuous part of the probability distribution of ~(t -1 / 2) _(Y t) given _(X0). The rate of convergence and the moment condition are the expected ones with respect to the i.i.d case. An application to the joint distribution of local times of a finite jump process is sketched.