Gaussian integrability of distance function under the Lyapunov condition

[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.

[学科分类] 统计和概率