60 citations · 145 across the 15 of their papers we have counts for
8 papers · 1 filter
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…
A Multilevel Approach towards Unbiased Sampling of Random Elliptic Partial Differential Equations
Xiaoou Li, Jingchen Liu
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to a…
Rare-event Simulation and Efficient Discretization for the Supremum of Gaussian Random Fields
Xiaoou Li, Jingchen Liu
In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field living on a compact set . We develop efficient computatio…
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…
On the conditional distributions and the efficient simulations of exponential integrals of Gaussian random fields
Jingchen Liu, Gongjun Xu
In this paper, we consider the extreme behavior of a Gaussian random field living on a compact set . In particular, we are interested in tail events associated with the i…
Efficient Simulation and Conditional Functional Limit Theorems for Ruinous Heavy-tailed Random Walks
Jose Blanchet, Jingchen Liu
The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed stochastic processes. Our changes-of-measure are param…
Tail approximations of integrals of Gaussian random fields
Jingchen Liu
This paper develops asymptotic approximations of as for a homogeneous smooth Gaussian random field, , living on a compact -dime…
Efficient Monte Carlo for high excursions of Gaussian random fields
Robert J. Adler, Jose H. Blanchet, Jingchen Liu
Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectat…