Strong convergence of the split-step theta method for neutral stochastic delay differential equations

DOI10.1016/j.apnum.2017.05.008zbMath1370.65004OpenAlexW2619774145MaRDI QIDQ2012631

Xiao Tang, Zhiping Yan, Ai-Guo Xiao

Publication date: 1 August 2017

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2017.05.008

zbMATH Keywords

strong convergencenumerical resultsplit-step theta methodneutral stochastic delay differential equationhighly nonlinear condition

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) 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)

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Cites Work

• Unnamed Item
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• Implicit numerical methods for highly nonlinear neutral stochastic differential equations with time-dependent delay
• Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations
• Highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama method
• Exponential mean square stability of numerical methods for systems of stochastic differential equations
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• Convergence and almost sure exponential stability of implicit numerical methods for a class of highly nonlinear neutral stochastic differential equations with constant delay
• Evaluation of conditional Wiener integrals by numerical integration of stochastic differential equations
• Convergence and stability of the split-step \(\theta \)-method for stochastic differential equations
• Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations
• Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters
• Approximations of solutions to neutral functional differential equations with nonlocal history conditions
• Strong convergence and stability of backward Euler-Maruyama scheme for highly nonlinear hybrid stochastic differential delay equation
• The split-step backward Euler method for linear stochastic delay differential equations
• Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching
• Higher-order implicit strong numerical schemes for stochastic differential equations
• On existence, uniqueness and numerical approximation for neutral equations with state-dependent delays
• Strong convergence of the split-step theta method for stochastic delay differential equations with nonglobally Lipschitz continuous coefficients
• Retarded differential equations
• Computational methods for quantitative finance. Finite element methods for derivative pricing
• Mean square stability and dissipativity of two classes of theta methods for systems of stochastic delay differential equations
• The Cox-Ingersoll-Ross model with delay and strong convergence of its Euler-Maruyama approximate solutions
• Fixed points and exponential stability for a stochastic neutral cellular neural network
• Strong convergence of split-step backward Euler method for stochastic differential equations with non-smooth drift
• New criteria on exponential stability of neutral stochastic differential delay equations
• Split-step \({\theta}\)-method for stochastic delay differential equations
• Numerical approximation of nonlinear neutral stochastic functional differential equations
• Mean square convergence of one-step methods for neutral stochastic differential delay equations
• Convergence rate of EM scheme for \normalfont𝑆𝐷𝐷𝐸𝑠
• The improved split-step backward Euler method for stochastic differential delay equations
• Numerical Solutions of Neutral Stochastic Functional Differential Equations
• One-Step Methods of any Order for Neutral Functional Differential Equations
• Numerical Solution of Implicit Neutral Functional Differential Equations
• Neutral Stochastic Differential Delay Equations with Markovian Switching
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations