一类随机积分延迟微分方程半隐式Milstein方法的稳定性
首发时间:2019-04-01
摘要:随机积分延迟微分方程被广泛地应用于生物、经济和机械等各个领域,研究其数值方法的稳定性具有重要科学意义和应用价值。本文对一类带Markov跳跃的随机积分延迟微分方程构造半隐式Milstein格式,证明了半隐式Milstein方法应用到方程上的稳定性,给出了方程MS-稳定(mean-square stability)和GMS-稳定(genarally mean-square stability)的条件。理论证明和数值试验说明了半隐式Milstein方法的有效性。
关键词: 带Markov跳跃的随机积分延迟微分方程 半隐式Milstein方法 MS-稳定 GMS-稳定 数值试验
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Stability of semi-implicit Milstein method for a class of stochastic delay integro-differential equations
Abstract:Stochastic delay integro-differential equations(SDIDE) are widely used in various fields such as biology, economy and machinery.It is of great scientific significance and application value to study the stability of its numerical methods.In this paper, we construct a semi-implicit Milstein scheme for a class of stochastic delay integro-differential equations with Markov jumps, and prove the stability of the semi-implicit Milstein method applied to equations.The conditions of MS-stable and GMS-stable are given.Theoretical proofs and numerical examples illustrating the validity of the semi-implicit Milstein method .
Keywords: stochastic delay Integro-differential equation with Markov Jump semi-implicit Milstein method MS-stable GMS-stable numerical experiment
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一类随机积分延迟微分方程半隐式Milstein方法的稳定性
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