Harnack不等式在Markov过程长时间行为研究中的应用

Application of Harnack inequality to long time asymptotics of Markov processes

本文使用Markov半群的无穷维Harnack不等式刻画Markov过程的长时间行为,建立可加泛函的极限定理,简化和放松了原有的条件.所获得的一般结果被应用于随机Hamilton系统和半线性随机偏微分方程,对于一类退化的扩散过程和无穷维扩散过程建立了所需的Harnack不等式,得到了相应的极限定理.

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 for degenerate diffusions as well as infinite-dimensional diffusions.