2015
DOI: 10.1016/j.amc.2015.05.041
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Exponential stability of numerical solution to neutral stochastic functional differential equation

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Cited by 16 publications
(9 citation statements)
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“…It should be highlighted that more attention has been paid to giving better conditions for stability of the analytic solution to the equation and its numerical solution. With the linear growth condition on drift coefficient, the EM numerical solution was shown to reproduce the exponential stability of the analytic solution for neutral stochastic functional (or delay) differential equation 18,19 . Several works showed that the linear growth condition was necessary to ensure the stability of the EM method 17,18,20,21 .…”
Section: Introductionmentioning
confidence: 99%
“…It should be highlighted that more attention has been paid to giving better conditions for stability of the analytic solution to the equation and its numerical solution. With the linear growth condition on drift coefficient, the EM numerical solution was shown to reproduce the exponential stability of the analytic solution for neutral stochastic functional (or delay) differential equation 18,19 . Several works showed that the linear growth condition was necessary to ensure the stability of the EM method 17,18,20,21 .…”
Section: Introductionmentioning
confidence: 99%
“…The theoretical results obtained have been analyzed in detail and some sufficient conditions have been presented. Some existing results, for example [8,21,[23][24][25][26][27][28], have been generalized. Meanwhile, the strong convergence for the theoretical solution and the numerical solution of such equations has been considered.…”
Section: Resultsmentioning
confidence: 99%
“…Recently, the exponential stability of the EM method for NSFDEs with jumps was analyzed in [16]. The almost surely and mean square exponential stability of numerical solutions for NSFDEs were considered in [23,27]. In [28], Zong et al analyzed the mean square exponential stability of the numerical solutions for NSFDEs.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Increasingly real-world systems are modeled by SFDEs of neutral type, as they represent systems which evolve in a random environment and whose evolution depends on the past states and derivatives of states of the systems through either memory or time delay. In the last decade, for SFDEs of neutral type, there are a large number of papers on, e.g., stochastic stability (see, e.g., [12,13,26]), on large fluctuations (see, e.g., [1]), on large deviation principle (see, e.g., [6]), on transportation inequality (see, e.g., [3]), to name a few.…”
Section: Introductionmentioning
confidence: 99%