Existence, uniqueness, almost sure polynomial stability of solution to a class of highly nonlinear pantograph stochastic differential equations and the Euler-Maruyama approximation

DOI10.1016/j.amc.2014.03.132zbMath1334.60117OpenAlexW2137286959MaRDI QIDQ275074

Marija Milošević

Publication date: 25 April 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2014.03.132

zbMATH Keywords

convergence in probabilityalmost sure polynomial stabilityEuler-Maruyama approximationnonlinear growth conditionpantograph stochastic differential equations

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Stability of solutions to ordinary differential equations (34D20)

Related Items (21)

Polynomial stability of exact solution and a numerical method for stochastic differential equations with time-dependent delay ⋮ Stochastic stability for pantograph multi-group models with dispersal and stochastic perturbation ⋮ Stability of numerical solution to pantograph stochastic functional differential equations ⋮ Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients ⋮ Stability of hybrid pantograph stochastic functional differential equations ⋮ Razumikhin-type theorems on polynomial stability of hybrid stochastic systems with pantograph delay ⋮ Almost sure exponential stability of numerical solutions for stochastic pantograph differential equations ⋮ Razumikhin-type theorems on the moment stability of the exact and numerical solutions for the stochastic pantograph differential equations ⋮ Ulam–Hyers stability of pantograph fractional stochastic differential equations ⋮ \(p\)th moment exponential stability of highly nonlinear neutral pantograph stochastic differential equations driven by Lévy noise ⋮ Stability of numerical solutions for the stochastic pantograph differential equations with variable step size ⋮ Razumikhin-type technique on stability of exact and numerical solutions for the nonlinear stochastic pantograph differential equations ⋮ Almost sure stability with general decay rate of exact and numerical solutions for stochastic pantograph differential equations ⋮ The \(p\)th moment asymptotical ultimate boundedness of pantograph stochastic differential equations with time-varying coefficients ⋮ Convergence and almost sure polynomial stability of the backward and forward-backward Euler methods for highly nonlinear pantograph stochastic differential equations ⋮ Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation ⋮ The partially truncated Euler-Maruyama method for nonlinear pantograph stochastic differential equations ⋮ The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise ⋮ \(p\)th moment exponential stability of neutral stochastic pantograph differential equations with Markovian switching ⋮ Pantograph stochastic differential equations driven by \(G\)-Brownian motion ⋮ General stabilization of non-autonomous hybrid systems with delays and random noises via delayed feedback control

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