Abstract
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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This research is partially supported by the NNSF of China (No. 11271093) and the NNSF of China (No. 91647204).
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Xu, L., Luo, J. Invariance of Closed Convex Sets for Stochastic Functional Differential Equations. Mediterr. J. Math. 15, 162 (2018). https://doi.org/10.1007/s00009-018-1199-4
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DOI: https://doi.org/10.1007/s00009-018-1199-4