39 citations · 503 across the 77 of their papers we have counts for
5 papers · 2 filters
Strong Feller properties for degenerate SDEs with jumps
Zhao Dong, Xuhui Peng, Yulin Song +1
Under full Hörmander's conditions, we prove the strong Feller property of the semigroup determined by an SDE driven by additive subordinate Brownian motion, where the drift is allo…
Harnack inequalities for SDEs driven by cylindrical -stable processes
Linlin Wang, Xicheng Zhang
By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotro…
Nonlocal Hormander's hypoellipticity theorem
Xicheng Zhang
Consider the following nonlocal integro-differential operator: for , $$ \cal L^{(α)}_{σ,b} f(x):=\mbox{p.v.} \int_{\mathbb{R}^d-\{0\}}\frac{f(x+σ(x)z)-f(x)}{|z|^{d+α}}d…
Gradient estimates for SDEs Driven by Multiplicative Lévy Noise
Feng-Yu Wang, Lihu Xu, Xicheng Zhang
Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative Lévy noise. In particular,…
Fundamental solution of kinetic Fokker-Planck operator with anisotropic nonlocal dissipativity
Xicheng Zhang
By using the probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic no…