Implicit numerical methods for neutral stochastic differential equations with unbounded delay and Markovian switching

DOI10.1016/j.amc.2018.11.037zbMath1429.65020OpenAlexW2902436898MaRDI QIDQ2008552

Maja Obradović

Publication date: 26 November 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2018.11.037

zbMATH Keywords

Markovian switchingconvergence in probabilitybackward and forward-backward Euler methodsglobal a.s. asymptotic exponential stabilityneutral stochastic differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic functional-differential equations (34K50) Ordinary differential equations and systems with randomness (34F05) 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

• Implicit numerical methods for highly nonlinear neutral stochastic differential equations with time-dependent delay
• Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler-Maruyama method
• Highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama method
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• Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions
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• An approximate method via Taylor series for stochastic functional differential equations
• Stability of stochastic differential equations with Markovian switching
• Exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching
• Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Stability of a random diffusion with linear drift
• Stability and boundedness of nonlinear hybrid stochastic differential delay equations
• Almost sure exponential stability of solutions to highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama approximation
• New criteria on exponential stability of neutral stochastic differential delay equations
• Approximate solutions of stochastic differential delay equations with Markovian switching
• Asymptotic properties of neutral stochastic differential delay equations
• Stochastic differential delay equations with jumps, under nonlinear growth condition
• Stochastic Differential Equations with Markovian Switching
• Khasminskii-Type Theorems for Stochastic Differential Delay Equations

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