Criteria for exponential convergence to quasi-stationary distributions and applications to multi-dimensional diffusions
Criteria for exponential convergence to quasi-stationary distributions and applications to multi-dimensional diffusions
复制标题
指数收敛到准平稳分布的标准及其在多维扩散中的应用
DOI：
10.1007/978-3-319-92420-5_5
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
D. Villemonais
中科院分区：
文献类型：
--
作者：
Nicolas Champagnat;K. Coulibaly;D. Villemonais
我们考虑一般的马尔可夫过程的吸收和提供的标准，确保指数收敛的分布的总变差的过程条件不被吸收。第一个是基于双边估计的过渡核的过程和第二个梯度估计的半群。我们将这些标准应用到多维扩散过程中的有界域的$\R^d$或在紧黎曼流形的边界，吸收在边界上。
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided estimates on the transition kernel of the process and the second one on gradient estimates on its semigroup. We apply these criteria to multi-dimensional diffusion processes in bounded domains of $\R^d$ or in compact Riemannian manifolds with boundary, with absorption at the boundary.