Approximation of invariant measure for damped stochastic nonlinear Schrödinger equation via an ergodic numerical scheme

DOI10.1007/s11118-016-9583-9zbMath1402.60085arXiv1509.09148OpenAlexW2963781534MaRDI QIDQ512837

Chuchu Chen, Jialin Hong, Xu Wang

Publication date: 2 March 2017

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.09148

zbMATH Keywords

error estimationergodicityinvariant measurenumerical schemestochastic Schrödinger equation

Mathematics Subject Classification ID

Computational methods for problems pertaining to probability theory (60-08) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (10)

Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations ⋮ Numerical ergodicity of two dimensional stochastic Navier-Stokes equations with Gaussian noise ⋮ A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations ⋮ High Order Conformal Symplectic and Ergodic Schemes for the Stochastic Langevin Equation via Generating Functions ⋮ CLT for approximating ergodic limit of SPDEs via a full discretization ⋮ Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic Scheme ⋮ Using Coupling Methods to Estimate Sample Quality of Stochastic Differential Equations ⋮ Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients ⋮ Parareal Exponential $\theta$-Scheme for Longtime Simulation of Stochastic Schrödinger Equations with Weak Damping ⋮ Stochastic differential equation with piecewise continuous arguments: Markov property, invariant measure and numerical approximation

Cites Work

• Unnamed Item
• Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation
• Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• A semi-discrete scheme for the stochastic nonlinear Schrödinger equation
• Non-Gaussian error probability in optical soliton transmission
• Approximation of the invariant measure with an Euler scheme for stochastic PDEs driven by space-time white noise
• An introduction to infinite-dimensional analysis
• Hypoelliptic second order differential equations
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs
• Weak order for the discretization of the stochastic heat equation
• Second-order discretization schemes of stochastic differential systems for the computation of the invariant law
• Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme
• Semilinear stochastic evolution equations with monotone nonlinearities

This page was built for publication: Approximation of invariant measure for damped stochastic nonlinear Schrödinger equation via an ergodic numerical scheme