Convergence of numerical solutions for variable delay differential equations driven by Poisson random jump measure

DOI10.1016/j.amc.2009.02.041zbMath1172.65008OpenAlexW2029471792MaRDI QIDQ1026318

Mao Wei

Publication date: 24 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.02.041

zbMATH Keywords

convergencestrong convergenceWiener processdelay differential equationsPoisson processsemi-implicit Euler methodcompensated Poisson random measure

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) 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 (9)

A compensated numerical method for solving stochastic differential equations with variable delays and random jump magnitudes ⋮ Discrete time waveform relaxation method for stochastic delay differential equations ⋮ Convergence and stability of implicit compensated Euler method for stochastic differential equations with Poisson random measure ⋮ Numerical solutions of stochastic differential delay equations with Poisson random measure under the generalized Khasminskii-type conditions ⋮ Numerical schemes for stochastic differential equations with variable and distributed delays: the interpolation approach ⋮ Numerical solutions of stochastic differential equations driven by Poisson random measure with non-Lipschitz coefficients ⋮ Taylor approximation of the solutions of stochastic differential delay equations with Poisson jump ⋮ The truncated theta-EM method for nonlinear and nonautonomous hybrid stochastic differential delay equations with Poisson jumps ⋮ Approximate solutions of hybrid stochastic pantograph equations with Levy jumps

Cites Work

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• The semi-implicit Euler method for stochastic differential delay equation with jumps
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Almost sure exponential stability of neutral stochastic differential difference equations
• Continuous \(\Theta\)-methods for the stochastic pantograph equation
• Weak discrete time approximation of stochastic differential equations with time delay
• Numerical solutions of stochastic differential delay equations under local Lipschitz condition
• One-step approximations for stochastic functional differential equations
• Exponential stability in \(p\)-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
• Probability with Martingales
• Numerical Solutions of Stochastic Functional Differential Equations

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