On mean square stability and dissipativity of split-step theta method for nonlinear neutral stochastic delay differential equations
type: Item
instance of: scholarly article
title: On mean square stability and dissipativity of split-step theta method for nonlinear neutral stochastic delay differential equations
zbMATH Open document ID: 1377.65008
DOI: 10.1155/2016/7397941
author: Haiyan Yuan
author: Cheng Song
author: Ji-Hong Shen
published in: Discrete Dynamics in Nature and Society
publication date: 2017-11-13T00:00:00Z
review text: Summary: A split-step theta (SST) method is introduced and used to solve the nonlinear neutral stochastic delay differential equations. The mean square asymptotic stability of the split-step theta (SST) method for nonlinear neutral stochastic delay differential equations is studied. It is proved that under the one-sided Lipschitz condition and the linear growth condition, the split-step theta method with \(\theta \in(1 / 2, 1]\) is asymptotically mean square stable for all positive step sizes, and the split-step theta method with \(\theta \in [0, 1 / 2]\) is asymptotically mean square stable for some step sizes. It is also proved in this paper that the split-step theta (SST) method possesses a bounded absorbing set which is independent of initial data, and the mean square dissipativity of this method is also proved.
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
zbMATH DE Number: 6806255
zbMATH Keywords: split-step theta method
zbMATH Keywords: nonlinear neutral stochastic delay differential equations
zbMATH Keywords: mean square asymptotic stability
zbMATH Keywords: mean square dissipativity
Wikidata QID: Q59123635
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/7397941
OpenAlex ID: W2485771410
cites work: Exponential stability in \(p\)-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
cites work: The ⊝-Maruyama scheme for stochastic functional differential equations with distributed memory term *
cites work: One-step approximations for stochastic functional differential equations
cites work: Discrete-time approximations of stochastic delay equations: the Milstein scheme.
cites work: Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation
cites work: Q4369402
cites work: Exponential stability of equidistant Euler-Maruyama approximations of stochastic differential delay equations
cites work: Q3707054
cites work: Q3137918
cites work: Numerical Solutions of Neutral Stochastic Functional Differential Equations
cites work: Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching
cites work: Q3085559
cites work: Numerical approximation of nonlinear neutral stochastic functional differential equations
cites work: Convergence of the semi-implicit Euler method for neutral stochastic delay differential equations with phase semi-Markovian switching
cites work: Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations
cites work: Exponential mean square stability of numerical methods for systems of stochastic differential equations
cites work: Convergence and stability of the split-step \(\theta \)-method for stochastic differential equations
cites work: The split-step backward Euler method for linear stochastic delay differential equations
cites work: Convergence and stability of the split-step backward Euler method for linear stochastic delay integro-differential equations
cites work: Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching
cites work: Dissipativity of Runge-Kutta methods for dynamical systems with delays
cites work: Dissipativity of multistep Runge-Kutta methods for dynamical systems with delays
description: scientific article; zbMATH DE number 6806255