Approximation and generic properties of McKean-Vlasov stochastic
equations with continuous coefficients
Abstract
We consider various approximation properties for systems driven by a Mc
Kean-Vlasov stochastic differential equations (MVSDEs) with continuous
coefficients, for which pathwise uniqueness holds. We prove that the
solution of such equations is stable with respect to small perturbation
of initial conditions, parameters and driving processes. Moreover, the
unique strong solutions may be constructed by an effective approximation
procedure. Finally we show that the set of bounded uniformly continuous
coefficients for which the corresponding MVSDE have a unique strong
solution is a set of second category in the sense of Baire.