A local limit theorem for densities of the additive component of a finite Markov Additive Process
arXiv:1306.5353 · doi:10.1016/j.spl.2013.05.032
Abstract
In this paper, we are concerned with centered Markov Additive Processes $\{(X_t,Y_t)\}_{t\in\T}$ where the driving Markov process $\{X_t\}_{t\in\T}$ 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 given . 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.
Additional material at arXiv:1305.5644 with some overlap