Comparison theorem for distribution-dependent neutral SFDEs. (English) Zbl 1468.65008
Summary: In this paper, the existence and uniqueness of strong solutions to distribution-dependent neutral SFDEs are proved. We give the conditions such that the order preservation of these equations holds. Moreover, we show these conditions are also necessary when the coefficients are continuous. Under sufficient conditions, the result extends the one in the distribution-independent case, and the necessity of these conditions is new even in distribution-independent case.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34K50 | Stochastic functional-differential equations |
Keywords:
comparison theorem; stochastic functional delay differential equations; distribution-dependent neutral SFDEs; existence and uniqueness; order preservation; Wasserstein distanceReferences:
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