Propagation of gibbsianness for infinite-dimensional diffusions with space-time interaction
- We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.
Metadaten| Verfasserangaben: | Sylvie RoellyGND, W. M. Ruszel |
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| ISSN: | 1024-2953 |
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| Titel des übergeordneten Werks (Englisch): | Markov processes and related fields |
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| Verlag: | Polymat |
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| Verlagsort: | Moscow |
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| Publikationstyp: | Wissenschaftlicher Artikel |
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| Sprache: | Englisch |
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| Jahr der Erstveröffentlichung: | 2014 |
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| Erscheinungsjahr: | 2014 |
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| Datum der Freischaltung: | 27.03.2017 |
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| Freies Schlagwort / Tag: | Girsanov formula; cluster expansion; infinite-dimensional diffusion; non-Markov drift; planar rotors; ultracontractivity |
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| Band: | 20 |
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| Ausgabe: | 4 |
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| Seitenanzahl: | 22 |
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| Erste Seite: | 653 |
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| Letzte Seite: | 674 |
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| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
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| Peer Review: | Referiert |
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