ON HALANAY-TYPE ANALYSIS OF EXPONENTIAL STABILITY FOR THE θ-MARUYAMA METHOD FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

DOI10.1142/S0219493705001341zbMath1081.65012MaRDI QIDQ5694405

Evelyn Buckwar, Christopher T. H. Baker

Publication date: 30 September 2005

Published in: Stochastics and Dynamics (Search for Journal in Brave)

zbMATH Keywords

exponential stabilitynumerical examplesEuler schemesstochastic differential delay equationsdiscrete time approximation

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Stochastic functional-differential equations (34K50) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (6)

A class of stochastic one-parameter methods for nonlinear SFDEs with piecewise continuous arguments ⋮ Stability of analytical and numerical solutions for nonlinear stochastic delay differential equations with jumps ⋮ Mean-square stability of stochastic age-dependent delay population systems with jumps ⋮ Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag ⋮ A two-parameter Milstein method for stochastic Volterra integral equations ⋮ Exponential stability in \(p\)-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations

Cites Work

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• MS-stability of the Euler--Maruyama method for stochastic differential delay equations
• Stability analysis of continuous implicit Runge-Kutta methods for Volterra integro-differential systems with unbounded delays
• Retarded differential equations
• Differential equations: Stability, oscillations, time lags
• Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Numerical Methods for Delay Differential Equations

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