Invariance of Closed Convex Sets for Stochastic Functional Differential Equations

被引：0
|
作者：
Liping Xu
Jiaowan Luo
机构：
[1] Guangzhou University,School of Mathematics and Information Sciences
[2] Yangtze University,School of Information and Mathematics
来源：
Mediterranean Journal of Mathematics | 2018年 / 15卷
关键词：
Stochastic invariance; stochastic functional differential equation; weak solution; oriented distance; 60H10; 93E03;
D O I：
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学科分类号：
摘要：
The invariance of a closed convex set K for weak solutions of stochastic functional differential equation is studied. Some necessary and sufficient conditions in terms of the distance functional to K are given. When in addition the boundary of K is smooth, our necessary and sufficient conditions reduce to two relations that have to be verified just on the boundary of K. The results in Da Prato and Frankowska (J Math Anal Appl 333:151–163, 2007) are generalized. An example is given to illustrate our main results.
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