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On Gibbsianness of infinite-dimensional diffusions

  • The authors analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the d-dimensional lattice. In the first part of the paper, these processes are characterized as Gibbs states on path spaces. In the second part of the paper, they study the Gibbsian character on R^{Z^d} of the law at time t of the infinite-dimensional diffusion X(t), when the initial law is Gibbsian. AMS Classifications: 60G15 , 60G60 , 60H10 , 60J60

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Author:Sylvie RoellyGND, David Dereudre
Document Type:Postprint
Year of Completion:2004
Publishing Institution:Universität Potsdam
Release Date:2006/03/17
Tag:Gibbs field; cluster expansion; infinite-dimensional Brownian diffusion
Source:Markov Processes and Related Fields. - 10 (2004), 3, S. 395 - 410
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik