8 citations · 27 across the 15 of their papers we have counts for
6 papers · 1 filter
Ergodicity for eventually continuous Markov--Feller semigroups on Polish spaces
Fuzhou Gong, Yong Liu, Yuan Liu +1
This paper investigates the ergodicity of Markov--Feller semigroups on Polish spaces, focusing on very weak regularity conditions, particularly the Cesàro eventual continuity. Firs…
The Poincaré inequality and quadratic transportation-variance inequalities
Yuan Liu
It is known that the Poincaré inequality is equivalent to the quadratic transportation-variance inequality (namely ), see Jourdain \cit…
A new characterization of quadratic transportation-information inequalities
Yuan Liu
It is known that a quadratic transportation-information inequality interpolates between the Talagrand's inequality and the log-Sobolev inequality (L…
A link between the log-Sobolev inequality and Lyapunov condition
Yuan Liu
We give an alternative look at the log-Sobolev inequality (LSI in short) for log-concave measures by semigroup tools. The similar idea yields a heat flow proof of LSI under some qu…
Gaussian integrability of distance function under the Lyapunov condition
Yuan Liu
In this note we give a direct proof of the Gaussian integrability of distance function as for some provided the Lyapunov condition holds for symme…
Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces
Fu-Zhou Gong, Yuan Liu
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equat…