48 citations · 128 across the 30 of their papers we have counts for
5 papers · 2 filters
Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradient
Renming Song, Longjie Xie, Yingchao Xie
By using Duhamel's formula, we prove sharp two-sided estimates for the heat kernel of spectral fractional Laplacian with time-dependent gradient perturbation in bounded d…
Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation
Peng Chen, Renming Song, Longjie Xie +1
We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{…
Well-posedness for SDEs driven by different type of noises
Yueling Li, Longjie Xie, Yingchao Xie
We show the existence and uniqueness of strong solutions for stochastic differential equation driven by partial -stable noise and partial Brownian noise with singular coefficien…
Ergodicity of stochastic differential equations with jumps and singular coefficients
Longjie Xie, Xicheng Zhang
We show the strong well-posedness of SDEs driven by general multiplicative Lévy noises with Sobolev diffusion and jump coefficients and integrable drift. Moreover, we also study th…
Pathwise uniqueness for a class of SPDEs driven by cylindrical -stable processes
Xiaobin Sun, Longjie Xie, Yingchao Xie
We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical -stable process with Hölder continuous drift, thus obtaining an infinite dim…