 Stability analysis of split-step θ-Milstein method for a class of n-dimensional stochastic differential equationsD. Ahmadian, O. Farkhondeh Rouz and L.V. Ballestra Applied Mathematics and Computation, 2019, vol. 348, issue C, 413-424 Abstract: In this paper, we introduce a split-step theta Milstein (SSTM) method for n-dimensional stochastic delay differential equations (SDDEs). The exponential mean-square stability of the numerical solutions is analyzed, and in accordance with previous findings, we prove that the method is exponentially mean-square stable if the employed time-step is smaller than a given and easily computable upper bound. In particular, according to our investigation, larger time-steps can be used in the case θ∈(12,1] than in the case θ∈[0,12]. Numerical results are presented which reveal that the SSTM method is conditionally mean-square stable and that in the case θ∈(12,1] the interval of time-steps for which the SSTM method is theoretically shown to be mean-square stable is significantly larger than in the case θ∈[0,12]. It is worth mentioning that the SSTM method has never been employed or analyzed for the numerical approximation of SDDEs, at least to the very best of our knowledge. Keywords: Split-step theta Milstein method; Exponential mean-square stability; Stochastic delay differential equations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:413-424 DOI: 10.1016/j.amc.2018.10.040 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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