Abstract

In this paper, a split-step theta (SST) method is introduced and analyzed for nonlinear neutral stochastic differential delay equations (NSDDEs). The asymptotic mean square stability of the split-step theta (SST) method is considered for nonlinear neutral stochastic differential equations. It is proved that, under the one-sided Lipschitz condition and the linear growth condition, for all positive stepsizes, the split-step theta method with \( \theta \in (1/2,1] \) is asymptotically mean square stable. The stability for the method with \( \theta \in [0,1/2] \) is also obtained under a stronger assumption. It further studies the mean square dissipativity of the split-step theta method with \( \theta \in (1/2,1] \) and proves that the method possesses a bounded absorbing set in mean square independent of initial data.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.