The Fleming-Viot Process with McKean-Vlasov Dynamics


Tough, O; Nolen, J


The Fleming-Viot particle system consists of N identical particles diffusing in a domain U⊂Rd. Whenever a particle hits the boundary ∂U, that particle jumps onto another particle in the interior. It is known that this system provides a particle representation for both the Quasi-Stationary Distribution (QSD) and the distribution conditioned on survival for a given diffusion killed at the boundary of its domain. We extend these results to the case of McKean-Vlasov dynamics. We prove that the law conditioned on survival of a given McKean-Vlasov process killed on the boundary of its domain may be obtained from the hydrodynamic limit of the corresponding Fleming-Viot particle system. We then show that if the target killed McKean-Vlasov process converges to a QSD as t→∞, such a QSD may be obtained from the stationary distributions of the corresponding N-particle Fleming-Viot system as N→∞.


Tough, Oliver, and James Nolen. “The Fleming-Viot Process with McKean-Vlasov Dynamics.” Electronic Journal of Probability 27 (August 3, 2022): 1–72.
Electronic Journal of Probability

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