Mean-square convergence of stochastic multi-step methods with variable step-size

DOI10.1016/j.cam.2006.12.014zbMath1131.60064OpenAlexW2126892829MaRDI QIDQ2468135

Thorsten Sickenberger

Publication date: 30 January 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.12.014

zbMATH Keywords

adaptive methodsmean-square convergencesmall noisestochastic linear multi-step methodsmean-square consistencymean-square numerical stabilitytwo-step-Maruyama methods

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) 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)

Related Items (12)

Strong convergence of split-step theta methods for non-autonomous stochastic differential equations ⋮ Convergence and stability of the split-step \(\theta \)-method for stochastic differential equations ⋮ Improved linear multi-step methods for stochastic ordinary differential equations ⋮ Double-implicit and split two-step Milstein schemes for stochastic differential equations ⋮ A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods ⋮ Deterministic implicit two-step Milstein methods for stochastic differential equations ⋮ Two-step Maruyama schemes for nonlinear stochastic differential delay equations ⋮ Mean square convergence of explicit two-step methods for highly nonlinear stochastic differential equations ⋮ Convergence and asymptotic stability of an explicit numerical method for non-autonomous stochastic differential equations ⋮ Local error estimates for moderately smooth problems. II: SDEs and SDAEs with small noise ⋮ Generalized two-step Maruyama methods for stochastic differential equations ⋮ Generalized two-step Milstein methods for stochastic differential equations

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