Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations
References (14)
- et al.
Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
J. Comput. Appl. Math.
(2005) Introduction to the numerical analysis of stochastic delay differential equations
J. Comput. Appl. Math.
(2000)- et al.
MS-stability of the Euler–Maruyama method for stochastic differential delay equations
Appl. Math. Comput.
(2004) - et al.
A modified Milstein scheme for approximation of stochastic delay differential equations with constant time lag
J. Comput. Appl. Math.
(2006) A note on exponential stability in pth mean of solutions of stochastic delay differential equations
J. Comput. Appl. Math.
(2007)- et al.
Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations
Nonlinear Analysis: Hybrid Systems
(2008) - et al.
An analysis of stability of Milstein method for stochastic differential equations with delay
Comput. Math. Appl.
(2006)
Cited by (43)
pth moment (p∈(0,1)) and almost sure exponential stability of the exact solutions and modified truncated EM method for stochastic differential equations
2020, Statistics and Probability LettersProjected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition
2020, Applied Mathematics and ComputationCitation Excerpt :In the past several decades, a number of numerical methods were investigated for SDDEs with one-sided Lipschitz drift and linearly growing diffusion coefficients (see [7–19] and references therein).
Numerical solution to highly nonlinear neutral-type stochastic differential equation
2019, Applied Numerical MathematicsCitation Excerpt :For instance, they are frequently used for the study of distributed networks containing lossless transmission lines (see [1,20]). So such models have received more and more attention (see [5,13,25]). Most neutral-type stochastic differential equations cannot be solved explicitly, so the numerical methods have received an increasing attention (see [17,19,22,26,28]).
Asymptotic exponential stability of modified truncated EM method for neutral stochastic differential delay equations
2018, Journal of Computational and Applied MathematicsExponential stability of the split-step θ-method for neutral stochastic delay differential equations with jumps
2017, Applied Mathematics and ComputationCitation Excerpt :Therefore, in order to achieve the exponential mean-square stability, more work need to be done for NSDDEs with jumps. For NSDDEs and SDDEs, some numerical methods and their stability have been investigated in [17,18,20,21,30], including the commonly used EM method, backward Euler–Maruyama (BEM) method and the stochastic θ method. However, they are basically one-step explicit or implicit method.
Strong convergence of the split-step theta method for neutral stochastic delay differential equations
2017, Applied Numerical Mathematics