中文摘要：

在可分Asplund空间中讨论随机集值隐函数的下半连续性及应用,所使用的工具主要有Ekeland变分原理、Fermat原理、Lipschitz函数的次微分以及次梯度的加法原理等.首先,给出随机集值隐函数的下半连续性成立的充分条件.其次,给出其在随机参数广义方程解映射的稳定性分析中的应用.所得结果改进了已有文献中的相关结果.

英文摘要：

This paper is mainly devoted to discussing lower semicontinuity of random implicit multifunctions in separable Asplund spaces.The tools involved are Ekeland＇s variational principle,Fermat＇s rules,subdifferentials of Lipschitzian functions and sum rules for basic and singular subgradients.Firstly,the new sufficient conditions for the lower semicontinuity of random implicit multifunctions are given.Secondly,applications to stability analysis of solution maps for random parametric generalized equations are given.The results obtained improve the corresponding known results in literature.