Gaussian integrability of distance function under the Lyapunov condition

Electronic Communications in Probability

Yuan Liu

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

In this note we give a direct proof of the Gaussian integrability of distance function as μeδd2(x,x0)<∞ for some δ>0 provided the Lyapunov condition holds for symmetric diffusionoperators, which answers a question by Cattiaux, Guillin, and Wu. The similar argument still works for diffusions processes with unbounded diffusion coefficients and for jump processes such as birth-death chains. An analogous discussion is also made under the Gozlan's condition.

【 授权许可】

CC BY