The Gibbs principle for Markov jump processes

This paper is devoted to derive a stochastic process version of the “Gibbs principle”. Namely, we calculate the law of a jump process (Xt, t ε [0, T] given the condition that the empirical energy function of N copies of the process, remains in some domain for all t ε [0, T], when N is large. The main tools are Csiszárʹs theory on conditional limit theorems and a law of large numbers in non-separable Banach spaces.