On Gibbsianness of infinite-dimensional diffusions

  • We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice $Z^{d} : X = (X_{i}(t), i ∈ Z^{d}, t ∈ [0, T], 0 < T < +∞)$. In a first part, these processes are characterized as Gibbs states on path spaces of the form $C([0, T],R)Z^{d}$. In a second part, we study the Gibbsian character on $R^{Z}^{d}$ of $v^{t}$, the law at time t of the infinite-dimensional diffusion X(t), when the initial law $v = v^{0}$ is Gibbsian.

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Metadaten
Author:David Dereudre, Sylvie Roelly
URN:urn:nbn:de:kobv:517-opus-52630
Series (Serial Number):Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2004, 01)
Document Type:Book
Language:English
Date of Publication (online):2011/06/17
Year of Completion:2004
Publishing Institution:Universität Potsdam
Release Date:2011/06/17
Tag:Gibbs field; cluster expansion; infinite-dimensional Brownian diffusion
RVK - Regensburg Classification:SI 990
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht