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.
Author details: | David DereudreORCiD, Sylvie RoellyGND |
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URN: | urn:nbn:de:kobv:517-opus-52630 |
Publication series (Volume number): | Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2004, 01) |
Publication type: | Monograph/Edited Volume |
Language: | English |
Publication year: | 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 |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
License (German): | Keine öffentliche Lizenz: Unter Urheberrechtsschutz |