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Abstract second-order damped McKean-Vlasov stochastic evolution equations
Stochastic Analysis and Applications
  • N. I. Mahmudov, Eastern Mediterranean University
  • Mark A. McKibben, West Chester University of Pennsylvania
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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.
Citation Information
N. I. Mahmudov and Mark A. McKibben. "Abstract second-order damped McKean-Vlasov stochastic evolution equations" Stochastic Analysis and Applications Vol. 24 Iss. 2 (2006) p. 303 - 328
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