Razumikhin-type theorem and mean square asymptotic behavior of the backward Euler method for neutral stochastic pantograph equations

DOI10.1186/1029-242X-2013-299zbMath1283.65008WikidataQ59301256 ScholiaQ59301256MaRDI QIDQ2436113

Zhanhua Yu

Publication date: 21 February 2014

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

numerical examplebackward Euler methodmean square stability\(p\)th moment asymptotic stabilityRazumikhin-type theoremneutral stochastic pantograph equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Stochastic functional-differential equations (34K50) Neutral functional-differential equations (34K40) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (3)

Convergence and stability of exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump ⋮ Stochastic approach for the solution of multi-pantograph differential equation arising in cell-growth model ⋮ Stability of numerical method for semi-linear stochastic pantograph differential equations

Cites Work

• Convergence of the semi-implicit Euler method for neutral stochastic delay differential equations with phase semi-Markovian switching
• Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations
• Exponential stability in mean square of neutral stochastic differential functional equations
• The \(\alpha \)th moment stability for the stochastic pantograph equation
• Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations
• On the \(p\)th moment exponential stability criteria of neutral stochastic functional differential equations
• Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching
• On the one-leg \(\theta \)-methods for solving nonlinear neutral functional differential equations
• Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations
• Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching
• Stability of Runge-Kutta methods for the generalized pantograph equation
• \(H_{\alpha}\)-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations
• Razumikhin-Type Theorems on Exponential Stability of Neutral Stochastic Differential Equations
• Asymptotic properties of neutral stochastic differential delay equations
• Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation

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