Two-step Milstein schemes for stochastic differential equations

DOI10.1007/S11075-014-9918-9zbMath1322.60138OpenAlexW2153162377MaRDI QIDQ2356076

M. J. Senosiain, Alicia Tocino

Publication date: 28 July 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-014-9918-9

zbMATH Keywords

stochastic differential equationsmean square stabilitystochastic Adams-Bashforth methodstochastic Adams-Moulton methodtwo-step Milstein schemes

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic integrals (60H05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (8)

Mean-square convergence and stability of two-step Milstein methods for stochastic differential equations with Poisson jumps ⋮ Mean-square stability of a constructed Third-order stochastic Runge--Kutta schemes for general stochastic differential equations ⋮ Two-step strong order 1.5 schemes for stochastic differential equations ⋮ Mean-square stability of split-step theta Milstein methods for stochastic differential equations ⋮ Deterministic implicit two-step Milstein methods for stochastic differential equations ⋮ Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs ⋮ Generalized two-step Maruyama methods for stochastic differential equations ⋮ Generalized two-step Milstein methods for stochastic differential equations

Cites Work

• Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance
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• A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods
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• A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise
• Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations
• Asymptotic mean-square stability of two-step Maruyama schemes for stochastic differential equations
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Multistep methods for SDEs and their application to problems with small noise
• Asymptotical mean square stability of an equilibrium point of some linear numerical solutions with multiplicative noise
• Numerical Analysis of Stochastic Schemes in Geophysics
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