Gaussian integrability of distance function under the Lyapunov condition

Abstract

In this note we give a direct proof of the Gaussian integrability of distance function as $\mu e^{\delta d^2(x,x_0)}<\infty$ for some $\delta >0$ provided the Lyapunov condition holds for symmetric diffusion Markov operators, which answers a question proposed in Cattiaux-Guillin-Wu [6, Page 295]. 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 arising from [9, Proposition 3.5].

11 pages, published, ECP. Some extensions to unbounded diffusions and jump processes have been added, and two referees' suggestions incorporated

References in corpus (4)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Stochastic differential equations with jumps
• Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities
• Some remarks on weighted logarithmic Sobolev inequality

Cited by in corpus (1)

• A new characterization of quadratic transportation-information inequalities