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分段连续型随机微分方程指数Euler方法的稳定性

刘国清,李唐海,邬德林,张玲

DEStech Transactions on Engineering and Technology Research（2021）

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Abstract
给出了线性分段连续型随机微分方程指数Euler方法的均方指数稳定性.经典的对稳定性理论分析,通常应用的是Lyapunov泛函理论,然而,应用该方程本身的特点和矩阵范数的定义给出了该方程精确解的均方稳定性.以往对于该方程应用隐式Euler方法得到对于任意步长数值解的均方稳定性,而应用显式Euler方法得到了相同的结果.最后,给出实例验证结论的有效性.
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Key words
linear stochastic differential equations,exponential euler method,stability,piecewise continuous arguments
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