Mean square convergence of one-step methods for neutral stochastic differential delay equations

DOI10.1016/j.amc.2008.07.034zbMath1155.65010OpenAlexW2032437586MaRDI QIDQ2518671

Haomin Zhang, Si-qing Gan

Publication date: 16 January 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2008.07.034

zbMATH Keywords

rate of convergenceconsistencynumerical methodsmean square convergenceLipschitz conditionsMilstein methodEuler-type methodsdrift-implicit one-step schemesneutral stochastic differential delay equations

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 (12)

The existence and uniqueness of mild solutions to stochastic differential equations with Lévy noise ⋮ Stochastic symplectic partitioned Runge-Kutta methods for stochastic Hamiltonian systems with multiplicative noise ⋮ On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations ⋮ On the approximations of solutions to neutral SDEs with Markovian switching and jumps under non-Lipschitz conditions ⋮ Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations ⋮ Numerical solutions to neutral stochastic delay differential equations with Poisson jumps under local Lipschitz condition ⋮ Convergence and asymptotical stability of numerical solutions for neutral stochastic delay differential equations driven by \(G\)-Brownian motion ⋮ High-order stochastic symplectic partitioned Runge-Kutta methods for stochastic Hamiltonian systems with additive noise ⋮ Strong convergence of the split-step theta method for neutral stochastic delay differential equations ⋮ Mean-square convergence of drift-implicit one-step methods for neutral stochastic delay differential equations with jump diffusion ⋮ Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations ⋮ Discrete gradient methods and linear projection methods for preserving a conserved quantity of stochastic differential equations

Cites Work

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• Stability of functional differential equations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Introduction to the numerical analysis of stochastic delay differential equations
• One-step approximations for stochastic functional differential equations

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