4 citations · 5 across the 10 of their papers we have counts for
11 papers
Long term convergence rate of Smoluchowski-Kramers approximation by Stein's method
Shiyu Liu, Wei Liu, Lihu Xu
We consider the following second-order stochastic differential equation on : \begin{equation*} dX_t^m=Y_t^mdt, \quad mdY_t^m=b(X_t^m)dt+σ(X_t^m)dB_t-Y^m_tdt, \end{…
Functional central limit theorem for Euler--Maruyama scheme with decreasing step sizes
Qiyang Pei, Lihu Xu
We consider the Euler--Maruyama (EM) scheme of a family of dissipative SDEs, whose step sizes are decreasing, and prove that the EM scheme weakly converge…
-convergence rate of EM schemes for invariant measures of supercritical stable SDEs
Peng Chen, Lihu Xu, Xiaolong Zhang +1
By establishing the regularity estimates for nonlocal Stein/Poisson equations under -order Hölder and dissipative conditions on the coefficients, we derive the -conve…
Robust estimation for high-dimensional time series with heavy tails
Yu Wang, Guodong Li, Zhijie Xiao +2
We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite -th moment with . To…
Error estimates between SGD with momentum and underdamped Langevin diffusion
Arnaud Guillin, Yu Wang, Lihu Xu +1
Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped La…
Quantitative diffusion approximation for the Neutral -Alleles Wright-Fisher Model with Mutations
Peng Chen, Jie Xiong, Lihu Xu +1
We apply a Lindeberg principle under the Markov process setting to approximate the Wright-Fisher model with neutral -alleles using a diffusion process, deriving an error rate ba…
Unbiased approximation of the ergodic measure for piecewise -stable Ornstein-Uhlenbeck processes arising in queueing networks
Xinghu Jin, Guodong Pang, Yu Wang +1
Piecewise -stable Ornstein-Uhlenbeck (OU) processes arising in queue networks usually do not have an explicit dissipation, which makes the related numerical methods such as Eule…
Phase transition in the EM scheme of an SDE driven by -stable noises with
Yu Wang, Yimin Xiao, Lihu Xu
We study in this paper the EM scheme for a family of well-posed critical SDEs with the drift and -stable noises. Specifically, we find that when the SDE is drive…
Approximation of the invariant measure for stable SDE by the Euler-Maruyama scheme with decreasing step-sizes
Peng Chen, Xinghu Jin, Yimin Xiao +1
Let be the solution of the stochastic differential equation where is a Lipsc…
The dynamics of the stochastic shadow Gierer-Meinhardt System
M. Winter, L. Xu, J. Zhai +1
We consider the dynamics of the stochastic shadow Gierer-Meinhardt system with one-dimensional standard Brownian motion. We establish the global existence and uniqueness of solutio…
Exponential ergodicity and regularity for equations with Lévy noise
E. Priola, A. Shirikyan, L. Xu +1
We prove exponential convergence to the invariant measure, in the total variation norm, for solutions of SDEs driven by -stable noises in finite and in infinite dimensions. Two…