39 citations · 503 across the 77 of their papers we have counts for
5 papers · 2 filters
Heat kernel and ergodicity of SDEs with distributional drifts
Xicheng Zhang, Guohuan Zhao
In this paper we consider the following SDE with distributional drift : where is a bounded conti…
Well-posedness of supercritical SDE driven by Lévy processes with irregular drifts
Zhen-Qing Chen, Xicheng Zhang, Guohuan Zhao
In this paper, we study the following time-dependent stochastic differential equation (SDE) in : $$ d X_{t}= σ_t(X_{t-}) d Z_t + b_t(X_{t})d t, \quad X_{0}=x\in {\bf R}^…
Heat kernels for time-dependent non-symmetric stable-like operators
Zhen-Qing Chen, Xicheng Zhang
When studying non-symmetric nonlocal operators $$ {\cal L} f(x) = \int_{{\bf R}^d} \left( f(x+z)-f(x)-\nabla f(x)\cdot z 1_{\{|z|\leq 1\}} \right) \frac{κ(x, z)}{|z|^{d+α}} d z , $…
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…
Heat Kernels for Non-symmetric Non-local Operators
Zhen-Qing Chen, Xicheng Zhang
We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat ker…