模糊随机微分方程解的存在唯一性

Existence and Uniqueness of Solutions for Fuzzy Stochastic Differential Equations

将实数空间上的随机微分方程推广到模糊数空间,即为模糊随机微分方程。本文用Picard迭代的方法证明了其解的存在唯一性定理,推广了现有文献的结果,并且给出Picard迭代近似解误差的估计式。

In this paper, stochastic differential equations in Euclid space are extended to the space of fuzzy numbers, and referred as fuzzy stochastic differential equations （FSDE）. A theorem of existence and uniqueness of solutions for FSDE is proved by Picard iteration procedure,which extends the results in the literature. Moreover, an estimate on the error of approximate solutions of the Picard iteration is given.