112,402 research outputs found
The enhanced Sanov theorem and propagation of chaos
We establish a Sanov type large deviation principle for an ensemble of
interacting Brownian rough paths. As application a large deviations for the
(-layer, enhanced) empirical measure of weakly interacting diffusions is
obtained. This in turn implies a propagation of chaos result in rough path
spaces and allows for a robust subsequent analysis of the particle system and
its McKean-Vlasov type limit, as shown in two corollaries.Comment: 42 page
A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows
In this article we set up a splitting variant of the JKO scheme in order to
handle gradient flows with respect to the Kantorovich-Fisher-Rao metric,
recently introduced and defined on the space of positive Radon measure with
varying masses. We perform successively a time step for the quadratic
Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao
distance. Exploiting some inf-convolution structure of the metric we show
convergence of the whole process for the standard class of energy functionals
under suitable compactness assumptions, and investigate in details the case of
internal energies. The interest is double: On the one hand we prove existence
of weak solutions for a certain class of reaction-advection-diffusion
equations, and on the other hand this process is constructive and well adapted
to available numerical solvers.Comment: Final version, to appear in SIAM SIM
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