Abstract Second-Order Damped McKean-Vlasov Stochastic Evolution Equations

Abstract We establish results concerning the global existence, uniqueness, approximate, and exact controllability of mild solutions for a class of abstract second-order stochastic evolution equations in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t. First-order equations of McKean-Vlasov type were first analyzed in the finite dimensional setting when studying diffusion processes, and then subsequently extended to the Hilbert space setting. The current manuscript provides a formulation of such results for second-order problems. Examples illustrating the applicability of the general theory are also provided.

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