Markov Additive Processes I. Eigenvalue Properties and Limit Theorems

Abstract

We consider a Markov additive process $\{(X_n, S_n): n = 0, 1,\ldots\}$, where $\{X_n\}$ is a M.C. on a general state space and $S_n$ is an $\mathbb{R}^d$-valued additive component. Limit theory for $S_n$ is studied via properties of the eigenvalues and eigenfunctions of the kernel of generating functions associated with the transition function of the process. The emphasis is on large deviation theory, but some other limit theorems are also given.