30 citations · 53 across the 8 of their papers we have counts for
9 papers
A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testing
Kevin H. Huang, Xing Liu, Andrew B. Duncan +1
We prove a convergence theorem for U-statistics of degree two, where the data dimension is allowed to scale with sample size . We find that the limiting distribution of a U-…
Strong approximation for fractional wave equation forced by fractional Brownian motion with Hurst parameter
Xing Liu
We consider the time discretization of fractional stochastic wave equation with Gaussian noise, which is negatively correlated. Major obstacles to design and analyze time discretiz…
Difference methods for time discretization of stochastic wave equation
Xing Liu
The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time di…
High-accuracy time discretization of stochastic fractional diffusion equation
Xing Liu
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper…
Higher order approximation for stochastic wave equation
Xing Liu, Weihua Deng
The infinitesimal generator (fractional Laplacian) of a process obtained by subordinating a killed Brownian motion catches the power-law attenuation of wave propagation. This paper…
Bayesian Probabilistic Numerical Integration with Tree-Based Models
Harrison Zhu, Xing Liu, Ruya Kang +3
Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The stand…
Numerical approximation for fractional diffusion equation forced by a tempered fractional Gaussian noise
Xing Liu, Weihua Deng
This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of…
First exit and Dirichlet problem for the nonisotropic tempered -stable processes
Xing Liu, Weihua Deng
This paper discusses the first exit and Dirichlet problems of the nonisotropic tempered -stable process . The upper bounds of all moments of the first exit position $\left|…
Numerical methods for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion
Xing Liu, Weihua Deng
In this paper, we study the numerical schemes for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion.…