LARGE DEVIATIONS FOR ERGODIC PROCESSES IN SPLIT SPACES

We study a family of stochastic additive functionals of Markov processes with locally independent increments switched by jump Markov processes in an asymptotic split phase space. Based on an average approximation, we obtain a large deviation result for this stochastic evolutionary system using a weak convergence approach. Examples, including compound Poisson processes, illustrate cases in which the rate function is calculated in an explicit form.