EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION-中国Betway体育网页登陆

摘要 Thepaperdevelopsexponentialstabilityoftheanalyticsolutionandconvergenceinprobabilityofthenumericalmethodforhighlynonlinearhybridstochasticpantographequation.Theclassicallineargrowthconditionisreplacedbypolynomialgrowthconditions,underwhichthereexistsauniqueglobalsolutionandthesolutionisalmostsurelyexponentiallystable.Onthebasisofaseriesoflemmas,thepaperestablishesanewcriteriononconvergenceinprobabilityoftheEuler-Maruyamaapproximatesolution.Thecriterionisverygeneralsothatmanyhighlynonlinearstochasticpantographequationscanobeytheseconditions.Ahighlynonlinearexampleisprovidedtoillustratethemaintheory.

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EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

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