Banach空间随机微分方程的样本最大、最小解的存在性

EXISTENCE OF SAMPLE MAXIMAL AND MINIMAL SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS IN BANACH SPACES

本文研究了Ｂａｎａｃｈ空间随机微分方程的初值问题的样本最大、最小解的存在性．利用熟知的关于多值映射的可测选择结果，得到了两个此类问题的样本最大。

In this paper, we studied the existence of sample maximal and minimal solutions of stochastic differential equations in Banach spaces. By means of a known result about measurable selections of multivated maps, two existence theorem on the sample maximal and minimal solutions of stochostic Cauchy problems are obtained.