Implicit numerical methods for highly nonlinear neutral stochastic differential equations with time-dependent delay

DOI10.1016/J.AMC.2014.07.042zbMath1335.65010OpenAlexW1986291802MaRDI QIDQ278433

Marija Milošević

Publication date: 2 May 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2014.07.042

zbMATH Keywords

backward and forward-backward Euler methodsglobal a.s. asymptotic exponential stabilityneutral stochastic differential equationsnonlinear growth conditionsone-sided Lipschitz conditiontime-dependent delay

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic functional-differential equations (34K50) Neutral functional-differential equations (34K40) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (11)

Almost sure and pth moment stability of uncertain differential equations with time-varying delay ⋮ Almost sure exponential stability of the \(\theta \)-Euler-Maruyama method, when \(\theta \in (\frac{1}{2},1)\), for neutral stochastic differential equations with time-dependent delay under nonlinear growth conditions ⋮ On stability of numerical solutions of neutral stochastic delay differential equations with time‐dependent delay ⋮ Backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay ⋮ Convergence and almost sure exponential stability of implicit numerical methods for a class of highly nonlinear neutral stochastic differential equations with constant delay ⋮ Stochastic \(H_{2}/H_\infty\) control of nonlinear systems with time-delay and state-dependent noise ⋮ Implicit numerical methods for neutral stochastic differential equations with unbounded delay and Markovian switching ⋮ Divergence of the backward Euler method for ordinary stochastic differential equations ⋮ Strong convergence of the split-step theta method for neutral stochastic delay differential equations ⋮ Mean square convergence of explicit two-step methods for highly nonlinear stochastic differential equations ⋮ Almost sure exponential stability of the θ-Euler-Maruyama method for neutral stochastic differential equations with time-dependent delay when θ ∈ [0; 1 2]

Cites Work

• Unnamed Item
• Highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama method
• An application of Taylor series in the approximation of solutions to stochastic differential equations with time-dependent delay
• Stability of nonlinear neutral stochastic functional differential equations
• Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions
• Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations
• Almost sure exponential stability of numerical solutions for stochastic delay differential equations
• Neutral stochastic functional differential equations with additive perturbations
• An approximate method via Taylor series for stochastic functional differential equations
• Almost sure exponential stability of neutral stochastic differential difference equations
• Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Almost sure exponential stability of solutions to highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama approximation
• New criteria on exponential stability of neutral stochastic differential delay equations
• The improved stability analysis of the backward Euler method for neutral stochastic delay differential equations
• A Less Strange Version of Milnor's Proof of Brouwer's Fixed-Point Theorem
• Analytic Proofs of the "Hairy Ball Theorem" and the Brouwer Fixed Point Theorem
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Asymptotic properties of neutral stochastic differential delay equations
• Stochastic differential delay equations with jumps, under nonlinear growth condition
• Stochastic Differential Equations with Markovian Switching
• Khasminskii-Type Theorems for Stochastic Differential Delay Equations

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