3 citations · 22 across the 18 of their papers we have counts for
18 papers
The Non-Gaussian to Gaussian Transition: Pointwise Heat Kernel Estimates and Optimal Convergence Rates
Xianming Liu, Chongyang Ren, Mingyan Wu
We establish uniform pointwise estimates for the densities of a family of -stable processes with respect to the index for some . In addition, we estimate t…
Synchronization by degenerate noise
Xianming Liu, Xu Sun
In this paper, we derive several criteria for (weak) synchronization by noise without the global swift transitivity property. Our sufficient conditions for (weak) synchronization a…
On the limit distribution for stochastic differential equations driven by cylindrical non-symmetric -stable Lévy processes
Ting Li, Hongbo Fu, Xianming Liu
This article deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical -stable process. Under suitable conditions, it is pro…
The random dynamical pitchfork bifurcation with additive Lévy noises
Ziying He, Xianming Liu
This paper concerns the effects of additive non-Gaussian Lévy noises on the pitchfork bifurcation. We consider two types of noises, -stable process and the truncated process. Un…
A Wong-Zakai Approximation of Stochastic Differential Equations Driven by a General Semimartingale
Xianming Liu, Guangyue Han
We examine a Wong-Zakai type approximation of a family of stochastic differential equations driven by a general cadlag semimartingale. For such an approximation, compared with the…
An Elementary Proof of a Classical Information-Theoretic Formula
Xianming Liu, Ronit Bustin, Guangyue Han +1
A renowned information-theoretic formula by Shannon expresses the mutual information rate of a white Gaussian channel with a stationary Gaussian input as an integral of a simple fu…