Convergence Rates of the Splitting Scheme for Parabolic Linear Stochastic Cauchy Problems

DOI10.1137/090761835zbMath1216.65006arXiv0906.2129OpenAlexW2123010497MaRDI QIDQ3084195

Sonja Cox, J. M. A. M. van Neerven

Publication date: 15 March 2011

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

Full work available at URL: https://arxiv.org/abs/0906.2129

zbMATH Keywords

convergenceBrownian motionBanach spaceanalytic semigroupssplitting schemestochastic evolution equations\(C_{0}\)-semigroupstochastic convolutionsLie-Trotter product formulalinear stochastic Cauchy problem

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Brownian motion (60J65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) 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) Transition functions, generators and resolvents (60J35)

Related Items (8)

Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes ⋮ Pathwise Hölder convergence of the implicit-linear Euler scheme for semi-linear SPDEs with multiplicative noise ⋮ Analysis of a Splitting Scheme for Damped Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise ⋮ Splitting schemes for FitzHugh-Nagumo stochastic partial differential equations ⋮ Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations ⋮ Convergence of an Operator Splitting Scheme for Abstract Stochastic Evolution Equations ⋮ Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations ⋮ A mild Itô formula for SPDEs

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