Open Access
2015 Gaussian integrability of distance function under the Lyapunov condition
Yuan Liu
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Electron. Commun. Probab. 20: 1-10 (2015). DOI: 10.1214/ECP.v20-3838


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 operators, 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.


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Yuan Liu. "Gaussian integrability of distance function under the Lyapunov condition." Electron. Commun. Probab. 20 1 - 10, 2015.


Accepted: 31 January 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1308.26023
MathSciNet: MR3314644
Digital Object Identifier: 10.1214/ECP.v20-3838

Primary: 26D10
Secondary: 60E15 , 60J60

Keywords: diffusion process , Gaussian integrability , jump process , Lyapunov condition

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