5 papers · 1 filter
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…
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…
Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs
Zhihui Liu, Xiaoming Wu
We construct a family of explicit tamed Euler--Maruyama (TEM) schemes, which can preserve the same Lyapunov structure for super-linear stochastic ordinary differential equations (S…
Strong convergence rates for long-time approximations of SDEs with non-globally Lipschitz continuous coefficients
Xiaoming Wu, Xiaojie Wang
This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients.Under certain non-globally Lipschitz conditions, a long-time version o…