Laplace approximations for large deviations of nonreversible Markov processes. The nondegenerate case
Let \(X_t\) be a Markov process with compact metric state space \(E\). The Markov process is not assumed reversible. Let \(F\) be a smooth function on the set of probability measures on \(E\); the precise definition of this concept is given in the paper. Denoting by \(L_T = {1 \over T} \int^T_0 \delta_{X_s} ds\) the empirical measures generated by \(X_t\), the authors obtain asymptotic expansions as \(T \to \infty\) for the exponential moments \(E_x \exp TF (L_T)\). The notation is too involved to be stated here; Section 5 of the paper presents examples illustrating the assumptions in a more concrete setting.
scientific article; zbMATH DE number 796541