most citedExponential mixing for some SPDEs with Lévy noise

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math.PR2011

Invariance measures of stochastic 2D Navier-Stokes equations driven by -stable processes

Zhao Dong, Lihu Xu, Xicheng Zhang

In this note we prove the well-posedness for stochastic 2D Navier-Stokes equation driven by general Lévy processes (in particular, -stable processes), and obtain the existence o…

math.PR2011

A Modified log-Harnack inequality and asymptotically strong Feller property

Lihu Xu

We introduce a new functional inequality, which is a modification of log-Harnack inequality established in [20] and [29], and prove that it implies the asymptotically strong Feller…

math.PR2010

Log-Harnack Inequality for Stochastic Burgers Equations and Applications

Feng-Yu Wang, Jiang-Lun Wu, Lihu Xu

By proving an -gradient estimate for the corresponding Galerkin approximations, the log-Harnack inequality is established for the semigroup associated to a class of stochastic…