论文标题
通过庞加莱的不平等和贝克里 - emery标准与准平台的融合
Convergence to quasi-stationarity through Poincaré inequalities and Bakry-Emery criteria
论文作者
论文摘要
本文旨在提供一些来自功能不平等的工具，以处理准平台，以吸收马尔可夫流程。首先，显示与合适的DOOB变换相关的庞加莱不平等如何需要将条件分布的指数融合到总变化中的准平台分布和$ 1 $ -WASSERSTEIN距离中。特别关注多维扩散过程，上述庞加莱的不平等是由易于检查的Bakry-émery条件所暗示的，具体取决于次马克维亚发电机的正确特征向量，这并不总是知道。在对潜力的其他假设下，有可能绕过这种缺乏知识，这表明经典的巴克里 - 典型条件需要指数级准良好性。
This paper aims to provide some tools coming from functional inequalities to deal with quasi-stationarity for absorbed Markov processes. First, it is shown how a Poincaré inequality related to a suitable Doob transform entails exponential convergence of conditioned distributions to a quasi-stationary distribution in total variation and in $1$-Wasserstein distance. A special attention is paid to multi-dimensional diffusion processes, for which the aforementioned Poincaré inequality is implied by an easier-to-check Bakry-Émery condition depending on the right eigenvector for the sub-Markovian generator, which is not always known. Under additional assumptions on the potential, it is possible to bypass this lack of knowledge showing that exponential quasi-ergodicity is entailed by the classical Bakry-Émery condition.
