An application of Taylor series in the approximation of solutions to stochastic differential equations with time-dependent delay

DOI10.1016/J.CAM.2011.04.009zbMath1222.65013OpenAlexW2031326290MaRDI QIDQ550108

Marija Milošević, Miljana Jovanović

Publication date: 8 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2011.04.009

zbMATH Keywords

Taylor approximation\(L^{p}\) and almost sure convergencestochastic differential equations with time-dependent delay

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) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (8)

Existence, uniqueness, almost sure polynomial stability of solution to a class of highly nonlinear pantograph stochastic differential equations and the Euler-Maruyama approximation ⋮ Implicit numerical methods for highly nonlinear neutral stochastic differential equations with time-dependent delay ⋮ A Taylor method for stochastic differential equations with time-dependent delay via the polynomial condition ⋮ On the approximations of solutions to stochastic differential equations under polynomial condition ⋮ 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 ⋮ Convergence and almost sure exponential stability of implicit numerical methods for a class of highly nonlinear neutral stochastic differential equations with constant delay ⋮ An explicit analytic approximation of solutions for a class of neutral stochastic differential equations with time-dependent delay based on Taylor expansion ⋮ Implicit numerical methods for neutral stochastic differential equations with unbounded delay and Markovian switching

Cites Work

• Unnamed Item
• Unnamed Item
• Exponential stability of equidistant Euler-Maruyama approximations of stochastic differential delay equations
• An approximate method via Taylor series for stochastic functional differential equations
• Feedback and delays in neurological diseases: A modeling study using dynamical systems
• An analytic approximation of solutions of stochastic differential equations
• Discrete-time approximations of stochastic delay equations: the Milstein scheme.
• An analytic approximate method for solving stochastic integrodifferential equations
• Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations
• Nonlinear flows of stochastic linear delay equations
• Weak approximation of stochastic differential delay equations

This page was built for publication: An application of Taylor series in the approximation of solutions to stochastic differential equations with time-dependent delay