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Pré-Publication, Document De Travail Année : 2022

Couplings of brownian motions with set-valued dual processes on riemannian manifolds

Résumé

The purpose of this paper is to construct a Brownian motion X_t taking values in a Riemannian manifold M , together with a compact valued process D_t such that, at least for small enough D-stopping time T and conditioned to the filtration of D_t up to time T , the law of X_T is the normalized Lebesgue measure on D_T. This intertwining result is a generalization of Pitman theorem. We first construct regular intertwined processes related to Stokes' theorem. Then using several limiting procedures we construct synchronous intertwined, free intertwined, mirror intertwined processes. The local times of the Brownian motion on the (morphological) skeleton or the boundary of D plays an important role. Several example with moving intervals, discs, annulus, symmetric convex sets are investigated.
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Dates et versions

hal-03037469 , version 1 (03-12-2020)
hal-03037469 , version 2 (07-07-2022)

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Marc Arnaudon, Koléhè Coulibaly-Pasquier, Laurent Miclo. Couplings of brownian motions with set-valued dual processes on riemannian manifolds. 2022. ⟨hal-03037469v2⟩
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