High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs

DOI10.1137/130935616zbMath1310.65007OpenAlexW2057711290MaRDI QIDQ2927824

Gilles Vilmart, Assyr Abdulle, Konstantinos C. Zygalakis

Publication date: 4 November 2014

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://archive-ouverte.unige.ch/unige:41847

zbMATH Keywords

stochastic differential equation convergence numerical example ergodicity invariant measure Runge-Kutta method backward error analysis weak order stochastic theta method modified differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) 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)

Related Items (28)

Efficient Numerical Algorithms for the Generalized Langevin Equation ⋮ A Uniformly Accurate Scheme for the Numerical Integration of Penalized Langevin Dynamics ⋮ High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise ⋮ Numerical Methods for Stochastic Simulation: When Stochastic Integration Meets Geometric Numerical Integration ⋮ Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds ⋮ Accurate and robust splitting methods for the generalized Langevin equation with a positive prony series memory kernel ⋮ Optimal explicit stabilized postprocessed \(\tau\)-leap method for the simulation of chemical kinetics ⋮ A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations ⋮ Ergodic SDEs on submanifolds and related numerical sampling schemes ⋮ CLT for approximating ergodic limit of SPDEs via a full discretization ⋮ Bridging the gap between constant step size stochastic gradient descent and Markov chains ⋮ Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models ⋮ The forward-backward envelope for sampling with the overdamped Langevin algorithm ⋮ Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme ⋮ Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic Scheme ⋮ Time Correlation Functions of Equilibrium and Nonequilibrium Langevin Dynamics: Derivations and Numerics Using Random Numbers ⋮ Accelerating Proximal Markov Chain Monte Carlo by Using an Explicit Stabilized Method ⋮ Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations ⋮ Unnamed Item ⋮ Approximation of invariant measure for damped stochastic nonlinear Schrödinger equation via an ergodic numerical scheme ⋮ Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics ⋮ Adaptive Thermostats for Noisy Gradient Systems ⋮ Invariant measures of the Milstein method for stochastic differential equations with commutative noise ⋮ Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations ⋮ Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs ⋮ Error estimates on ergodic properties of discretized Feynman-Kac semigroups ⋮ Accurate and Efficient Splitting Methods for Dissipative Particle Dynamics ⋮ Stochastic differential equation with piecewise continuous arguments: Markov property, invariant measure and numerical approximation

This page was built for publication: High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs