Exponential stability of equidistant Euler-Maruyama approximations of stochastic differential delay equations

DOI10.1016/j.cam.2005.11.035zbMath1114.65005OpenAlexW2043241145MaRDI QIDQ859891

Xuerong Mao

Publication date: 22 January 2007

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.2005.11.035

zbMATH Keywords

Brownian motionstochastic flowItô's formulamean-square stabilityEuler-Maruyama's method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) 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

• Random differential inequalities
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Some issues in discrete approximate solution for stochastic differential equations
• General theorems for numerical approximation of stochastic processes on the Hilbert space \(H_2([0,T, \mu,\mathbb{R}^d)\)]
• Introduction to the numerical analysis of stochastic delay differential equations
• Numerical solutions of stochastic differential delay equations under local Lipschitz condition
• Stability of regime-switching stochastic differential equations
• Exponential stability in \(p\)-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
• Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations
• The Invariance of Asymptotic Laws of Linear Stochastic Systems under Discretization
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• The mean-square stability of numerical methods for solving stochastic differential equations
• Asymptotic stability and spiraling properties for solutions of stochastic equations
• Numerical Solutions of Stochastic Functional Differential Equations
• Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations
• Robustness of exponential stability of stochastic differential delay equations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Asymptotical mean square stability of an equilibrium point of some linear numerical solutions with multiplicative noise
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