Short-Time Gibbsianness for Infinite-Dimensional Diffusions with Space-Time Interaction

Frank Redig, Sylvie Rœlly, Wioletta Ruszel

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

We consider a class of infinite-dimensional diffusions where the interaction between the components has a finite extent both in space and time. We start the system from a Gibbs measure with a finite-range uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t0 > 0 such that the distribution at time t ≤ t0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.
Original languageEnglish
Pages (from-to)1124-1144
Number of pages21
JournalJournal of Statistical Physics
Volume138
Issue number6
DOIs
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • Infinite-dimensional diffusion
  • Cluster expansion
  • Time-reversal
  • Non-Markovian drift
  • Girsanov formula
  • Delay equations

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