| Abstract: |
| We investigate Mean-Field Stochastic Differential Equations (MFSDEs), where the coefficients depend on both the state and the marginal distribution of the solution. Under the assumption of global Lipschitz continuity of the coefficients in both arguments, the existence and uniqueness of a strong solution are well-established.
This paper addresses the topological structure of the set of continuous coefficients that yield unique strong solutions and convergent successive approximations. We prove that this set is residual within the Baire space of uniformly continuous functions, implying its genericity in a topological sense. Moreover, we establish the generic property of convergence of Picard successive approximations and the Euler numerical scheme using similar techniques. |
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