Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations

DOI10.1016/j.cam.2014.02.033zbMath1293.65011arXiv1301.5389OpenAlexW2592112716MaRDI QIDQ396243

Desheng Wang, Ai-Guo Xiao, Si-qing Gan

Publication date: 8 August 2014

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

Full work available at URL: https://arxiv.org/abs/1301.5389

zbMATH Keywords

backward Euler methodasymptotic contractivity in mean squarecontractivity in mean squarenonlinear stochastic delay differential equationstability in mean square

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic functional-differential equations (34K50) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (14)

The asymptotic behavior of solutions for stochastic evolution equations with pantograph delay ⋮ Strong convergence and stability of the split-step theta method for highly nonlinear neutral stochastic delay integro differential equation ⋮ Asymptotic mean-square stability of explicit Runge-Kutta Maruyama methods for stochastic delay differential equations ⋮ Delay dependent asymptotic mean square stability analysis of the stochastic exponential Euler method ⋮ On strong convergence of explicit numerical methods for stochastic delay differential equations under non-global Lipschitz conditions ⋮ Stability of stochastic SIRS epidemic models with saturated incidence rates and delay ⋮ Theta schemes for SDDEs with non-globally Lipschitz continuous coefficients ⋮ Unnamed Item ⋮ Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients ⋮ Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs ⋮ Delay dependent stability of stochastic split-step \(\theta\) methods for stochastic delay differential equations ⋮ Strong convergence of the split-step theta method for neutral stochastic delay differential equations ⋮ A two-parameter Milstein method for stochastic Volterra integral equations ⋮ Numerical solutions of SDEs with Markovian switching and jumps under non-Lipschitz conditions

Uses Software

• RODAS

Cites Work

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• Numerical methods for nonlinear stochastic differential equations with jumps
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• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations

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