Stochastically stable one-step approximations of solutions of stochastic ordinary differential equations

DOI10.1016/S0168-9274(02)00141-1zbMath1015.65003MaRDI QIDQ1861961

Rózsa Horváth-Bokor

Publication date: 10 March 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

strong convergenceWiener processesnumerical stabilityone-step methodstochastic ordinary differential equationsIto vector stochastic differential equation

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 (8)

The composite Milstein methods for the numerical solution of Itô stochastic differential equations ⋮ Solving the stochastic differential systems with modified split-step Euler-Maruyama method ⋮ Convergence and asymptotic stability of the explicit Steklov method for stochastic differential equations ⋮ T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise ⋮ Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations ⋮ The composite Milstein methods for the numerical solution of Stratonovich stochastic differential equations ⋮ Exponential mean-square stability of numerical solutions for stochastic delay integro-differential equations with Poisson jump ⋮ The Strong Convergence and Numerical Stability of Multistep Approximations of Solutions of Stochastic Ordinary Differential Equations

Cites Work

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• Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations
• High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Order Conditions of Stochastic Runge--Kutta Methods by B-Series
• Asymptotically Efficient Runge-Kutta Methods for a Class of Itô and Stratonovich Equations
• A Theorem on the Order of Convergence of Mean-Square Approximations of Solutions of Systems of Stochastic Differential Equations
• Balanced Implicit Methods for Stiff Stochastic Systems

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