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arXiv · 1306.5353

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

Loïc Hervé·James Ledoux
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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 $t^{-1/2}Y_t$ given $X_0$. 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.

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Loïc Hervé, James Ledoux. 2013-06-22. A local limit theorem for densities of the additive component of a finite Markov Additive Process. https://doi.org/10.1016/j.spl.2013.05.032

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