Abstract
In this paper, long time asymptotics and limit theorems of additive functionals are investigated for Markov processes by using the dimension-free Harnack inequality,such that existing conditions are simplified and relaxed. The general result is applied to the stochastic Hamiltonian systems and semilinear stochastic partial differential equations such that limit theorems are proved fordegenerate diffusions as well as infinite-dimensional diffusions.
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