Large deviation principle for additive functionals of semi-Markov processes

A large deviation principle (LDP) for a class of additive functionals of semi-Markov processes and their associated Markov renewal processes is studied via an almost sure functional central limit theorem. The rate function corresponding to the deviations from the paths of the corresponding empirical processes with logarithmic averaging is determined as a relative entropy with respect to the Wiener measure on D[0, infinity). A martingale decomposition for additive functionals of Markov renewal processes is employed.