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- W3005983831 abstract "In this article we introduce several kinds of easily implementable explicit schemes, which are amenable to Khasminski's techniques and are particularly suitable for highly nonlinear stochastic differential equations (SDEs). We show that without additional restriction conditions except those which guarantee the exact solutions possess their boundedness in expectation with respect to certain Lyapunov functions, the numerical solutions converge strongly to the exact solutions in finite-time. Moreover, based on the nonnegative semimartingale convergence theorem, positive results about the ability of explicit numerical approximation to reproduce the well-known LaSalle-type theorem of SDEs are proved here, from which we deduce the asymptotic stability of numerical solutions. Some examples and simulations are provided to support the theoretical results and to demonstrate the validity of the approach." @default.
- W3005983831 created "2020-02-24" @default.
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- W3005983831 date "2020-02-16" @default.
- W3005983831 modified "2023-10-18" @default.
- W3005983831 title "Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations" @default.
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- W3005983831 doi "https://doi.org/10.48550/arxiv.2002.06756" @default.
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