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The Fleming-Viot Process with McKean-Vlasov Dynamics

Publication ,  Journal Article
Tough, O; Nolen, J
Published in: Electronic Journal of Probability
August 3, 2022

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→∞.

Duke Scholars

Published In

Electronic Journal of Probability

DOI

ISSN

1083-6489

Publication Date

August 3, 2022

Volume

27

Start / End Page

1 / 72

Publisher

Institute of Mathematical Statistics

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0105 Mathematical Physics
  • 0104 Statistics
 

Citation

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Tough, O., & Nolen, J. (2022). The Fleming-Viot Process with McKean-Vlasov Dynamics. Electronic Journal of Probability, 27, 1–72. https://doi.org/10.1214/22-EJP820
Tough, Oliver, and James Nolen. “The Fleming-Viot Process with McKean-Vlasov Dynamics.” Electronic Journal of Probability 27 (August 3, 2022): 1–72. https://doi.org/10.1214/22-EJP820.
Tough O, Nolen J. The Fleming-Viot Process with McKean-Vlasov Dynamics. Electronic Journal of Probability. 2022 Aug 3;27:1–72.
Tough, Oliver, and James Nolen. “The Fleming-Viot Process with McKean-Vlasov Dynamics.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, Aug. 2022, pp. 1–72. Manual, doi:10.1214/22-EJP820.
Tough O, Nolen J. The Fleming-Viot Process with McKean-Vlasov Dynamics. Electronic Journal of Probability. Institute of Mathematical Statistics; 2022 Aug 3;27:1–72.

Published In

Electronic Journal of Probability

DOI

ISSN

1083-6489

Publication Date

August 3, 2022

Volume

27

Start / End Page

1 / 72

Publisher

Institute of Mathematical Statistics

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0105 Mathematical Physics
  • 0104 Statistics