Mémoires de la SMF N° 171/2021
On the evolution by duality of domains on manifolds
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- Nombre de pages110
- PrésentationBroché
- FormatGrand Format
- Poids0.325 kg
- Dimensions17,5 cm × 24,0 cm × 0,9 cm
- ISBN978-2-85629-935-7
- EAN9782856299357
- Date de parution01/01/2022
- ÉditeurSociété Mathématique de France
Résumé
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),TE(0,T) which are intertwining dual processes for X (where T 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)),tE(o,t)] 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.
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.
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),TE(0,T) which are intertwining dual processes for X (where T 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)),tE(o,t)] 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.
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.