Couplings of brownian motions with set-valued dual processes on riemannian manifolds
MICLO, Laurent
Toulouse School of Economics [TSE-R]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Toulouse School of Economics [TSE-R]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
MICLO, Laurent
Toulouse School of Economics [TSE-R]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
< Reduce
Toulouse School of Economics [TSE-R]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Language
en
Article de revue
This item was published in
Journal de l'École polytechnique — Mathématiques. 2024-02-20, vol. 11, p. 473-522
École polytechnique
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Stochastic mean curvature evolutions
Couplings of primal and dual processes
Set-valued dual processes
Intertwining relations
Brownian motions on Riemannian manifolds
Boundary and skeleton local times
Generalized Pitman theorem
ANR Project
Toulouse Graduate School défis en économie et sciences sociales quantitatives - ANR-17-EURE-0010
Origin
Hal imported