Abstract
In this paper, a stochastic linear theta (SLT) method is introduced and analyzed for neutral stochastic differential delay equations (NSDDEs). We give some conditions on neutral item, drift and diffusion coefficients, which admit that the diffusion coefficient can be highly nonlinear and does not necessarily satisfy a linear growth or global Lipschitz condition. It is proved that, for all positive stepsizes, the SLT method with θ∈[12,1] is asymptotically mean stable and so is θ∈[0,12) under a stronger assumption. Furthermore, we consider the split-step theta (SST) method and obtain a similar but better result. That is, the SST method with θ∈[12,1] is exponentially mean stable and so is θ∈[0,12). Finally, two numerical examples are given to show the efficiency of the obtained results.
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 callDisclaimer: 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.
