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A stochastic McKean-Vlasov equation for absorbing diffusions on the half-line

Abstract:

We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes large, the empirical measure of the population converges to the solution of a nonlinear stochastic heat equation with Dirichlet boundary condition. The diffusion coeffcients are allowed to have finitely many discontinuities (piecewise Lipschitz) and we prov...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1214/16-AAP1256

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Department:
St Annes College
Heilbronn Institute for Mathematical Research More from this funder
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Annals of Applied Probability Journal website
Volume:
27
Issue:
5
Pages:
2698-2752
Publication date:
2017-11-16
Acceptance date:
2016-10-30
DOI:
ISSN:
1050-5164
Pubs id:
pubs:664228
URN:
uri:5ffaf1ba-d012-44cf-a375-d4569f98a019
UUID:
uuid:5ffaf1ba-d012-44cf-a375-d4569f98a019
Local pid:
pubs:664228

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