8 papers
Uniform-in-Time Weak and Ergodic Error Estimates of a Nonlinearity-Explicit Full Discretization for Superlinear SPDEs Driven by Multiplicative Noise
Jingjing Cai, Zhihui Liu, Xiaoming Wu
For a class of superlinear SPDEs driven by multiplicative noise, we prove an (essentially) sharp uniform-in-time (UIT) weak convergence rate for the nonlinearity-explicit Galerkin…
Uniform-in-time Strong Error Estimates of Tamed-FEM to Superlinear SPDEs driven by Multiplicative Noise
Jingjing Cai, Zhihui Liu
We establish sharp, uniform-in-time strong error estimates for a nonlinearity-explicit tamed finite element method (FEM) applied to a class of superlinear stochastic partial differ…
Inversions of stochastic processes from ergodic measures of Nonlinear SDEs
Hongyu Liu, Zhihui Liu
We introduce and analyze a novel class of inverse problems for stochastic dynamics: Given the ergodic invariant measure of a stochastic process governed by a nonlinear stochastic o…
Ergodic Estimates of One-Step Numerical Approximations for Superlinear SODEs
Xin Liu, Zhihui Liu
This paper establishes the first-order convergence rate for the ergodic error of numerical approximations to a class of stochastic ODEs (SODEs) with superlinear coefficients and mu…
Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs
Zhihui Liu, Xiaojie Wang, Xiaoming Wu +1
A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preser…
Weak Error Estimates of Ergodic Approximations for Monotone Jump-diffusion SODEs
Zhihui Liu, Xiaoming Wu
We first derive the exponential ergodicity of the stochastic theta method (STM) with for monotone jump-diffusion stochastic ordinary differential equations (SODEs) u…