Large deviations of uniformly recurrent Markov additive processes (Q1081960)

A detailed discussion on the large deviation theory of Markov additive (MA) processes is presented here. Besides a logarithmic large deviation result, also sharper limit theorems (including exact upper and lower bounds) are derived. To do so, the authors introduce conjugate MA- processes, possessing a useful ''twisting'' property, and they develop certain local limit theorems for the latter, making use of the regenerative structure of the process. Several examples and special cases of the general theory, besides others e.g. MA-processes with finite state space or Brownian motion on a circle, are given for illustration. Finally, a representation of the logarithmic large deviation limits is given in terms of Kullback-Leibler information numbers.