A generalization of the Freidlin–Wentcell theorem on averaging of Hamiltonian systems

In this paper, we generalize the classical Freidlin-Wentzell’s theorem for random perturbations of Hamiltonian systems. (Probability Theory and Related Fields 128 (2004) 441–466), M.Freidlin M.Weber generalized original result in sense that coefficient noise term is no longer identity matrix but a state-dependent taking drift into consideration. We by adding converges uniformly to 0 on any compact sets as ? tends considering which contains two parts, mapping 0. proof, adapt new way prove weak convergence inside edge constructing an auxiliary process modify proof 441–466) when proving gluing condition.