On the evolution by duality of domains on manifolds

Abdoulaye Koléhè Coulibaly-Pasquier () and Laurent Miclo ()
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Abdoulaye Koléhè Coulibaly-Pasquier: IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique
Laurent Miclo: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: On a manifold, consider an elliptic diffusion X admitting an invariant measure μ. The goal of this paper is to introduce and investigate the first properties of stochastic domain evolutions (Dt)t∈[0,τ] which are intertwining dual processes for X (where τ is an appropriate positive stopping time before the potential emergence of singularities). They provide an extension of Pitman's theorem, as it turns out that (μ(Dt))t∈[0,τ] is a Bessel-3 process, up to a natural time-change. When X is a Brownian motion on a Riemannian manifold, the dual domain-valued process is a stochastic modification of the mean curvature flow to which is added an isoperimetric ratio drift to prevent it from collapsing into singletons.

Keywords: Diffusions elliptiques; Variétés riemanniennes; Dynamiques stochastiques de domaines; Dualité par entrelacement; Processus de Bessel; Flots par courbure moyenne modifiés; Espaces à courbure constante (search for similar items in EconPapers)
Date: 2022-01-01
Note: View the original document on HAL open archive server: https://hal.science/hal-03671574v1
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Published in Société mathématique de France, 171, 110 p., 2022, 978-2-85629-935-7. ⟨10.24033/msmf.479⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03671574

DOI: 10.24033/msmf.479

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