On a Monte Carlo scheme for some linear stochastic partial differential equations

DOI10.1515/mcma-2021-2088zbMath1486.65010OpenAlexW3172956153WikidataQ115235979 ScholiaQ115235979MaRDI QIDQ2040471

Akihiro Tanaka, Takuya Nakagawa

Publication date: 14 July 2021

Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/mcma-2021-2088

zbMATH Keywords

computational methodstochastic partial differential equation

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Monte Carlo methods (65C05) White noise theory (60H40) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (1)

Unconditionally stable Monte Carlo simulation for solving the multi-dimensional Allen-Cahn equation

Cites Work

• Unnamed Item
• Weak convergence analysis of the linear implicit Euler method for semilinear stochastic partial differential equations with additive noise
• Weak approximation of the stochastic wave equation
• Forward-backward stochastic differential equations and their applications
• Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations
• Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients
• Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient
• Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations
• Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients
• Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation
• Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs
• Weak convergence for a spatial approximation of the nonlinear stochastic heat equation
• Weak approximation of stochastic partial differential equations: the nonlinear case
• Finite element and difference approximation of some linear stochastic partial differential equations
• Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin Discretization
• Probability
• Weak error analysis for semilinear stochastic Volterra equations with additive noise
• Stochastic Equations in Infinite Dimensions

This page was built for publication: On a Monte Carlo scheme for some linear stochastic partial differential equations