Invariance of Closed Convex Sets for Stochastic Functional Differential Equations

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.