24 citations · 24 across the 4 of their papers we have counts for
4 papers
Moderate Deviation for Random Elliptic PDEs with Small Noise
Xiaoou Li, Jingchen Liu, Jianfeng Lu +1
Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsi…
Extreme Analysis of a Non-convex and Nonlinear Functional of Gaussian Processes -- On the Tail Asymptotics of Random Ordinary Differential Equations
Jingchen Liu, Xiang Zhou
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to…
An Explicit Cross Entropy Scheme for Mixtures
Hui Wang, Xiang Zhou
The key issue in importance sampling is the choice of the alternative sampling distribution, which is often chosen from the exponential tilt family of the underlying distribution.…
Escaping from an attractor: Importance sampling and rest points I
Paul Dupuis, Konstantinos Spiliopoulos, Xiang Zhou
We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complic…