Subgeometric rates of convergence of f-ergodic strong Markov processes
Subgeometric rates of convergence of f-ergodic strong Markov processes
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DOI：
10.1016/j.spa.2008.03.007
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发表时间：
2006-05
影响因子：
1.4
通讯作者：
R. Douc;G. Fort;A. Guillin
中科院分区：
文献类型：
--
作者：
R. Douc;G. Fort;A. Guillin
本文给出了马氏过程泛函的上鞅性质的一个条件，该条件包含（a）强马氏过程在次几何速率下的f-遍历性和（B）积分（有界）泛函的中偏差原理.给出了广义生成元上漂移不等式的等价条件。有关的结果（f，r）-正则性的过程中，一些骨架链和预解链的。具体过程的应用被认为是，包括椭圆随机微分方程，朗之万扩散，亚椭圆随机阻尼哈密顿系统和存储模型。
We provide a condition in terms of a supermartingale property for a functional of the Markov process, which implies (a) f-ergodicity of strong Markov processes at a subgeometric rate, and (b) a moderate deviation principle for an integral (bounded) functional. An equivalent condition in terms of a drift inequality on the extended generator is also given. Results related to (f,r)-regularity of the process, of some skeleton chains and of the resolvent chain are also derived. Applications to specific processes are considered, including elliptic stochastic differential equations, Langevin diffusions, hypoelliptic stochastic damping Hamiltonian systems and storage models.