Statistics of transitions for Markov chains with periodic forcing

Abstract

The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular a functional Central Limit Theorem can be proven for the number of transitions between two states chosen in the whole finite state space of the Markov chain. An application to the stochastic resonance is presented.