On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations
Joint Authors
Song, Cheng
Shen, Ji-Hong
Yuan, Haiyan
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-08-07
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
A split-step theta (SST) method is introduced and used to solve the nonlinear neutral stochastic delay differential equations (NSDDEs).
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 θ∈(1/2,1] is asymptotically mean square stable for all positive step sizes, and the split-step theta method with θ∈[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.
American Psychological Association (APA)
Yuan, Haiyan& Shen, Ji-Hong& Song, Cheng. 2016. On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations. Discrete Dynamics in Nature and Society،Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1103548
Modern Language Association (MLA)
Yuan, Haiyan…[et al.]. On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations. Discrete Dynamics in Nature and Society No. 2016 (2016), pp.1-8.
https://search.emarefa.net/detail/BIM-1103548
American Medical Association (AMA)
Yuan, Haiyan& Shen, Ji-Hong& Song, Cheng. On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations. Discrete Dynamics in Nature and Society. 2016. Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1103548
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1103548