Finite and infinite systems of interacting diffusions

J. T. Cox, Andreas Greven, Tokuzo Shiga

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

We study the problem of relating the long time behavior of finite and infinite systems of locally interacting components. We consider in detail a class of lincarly interacting diffusions x(t)={x i (t), i ∈ ℤ d } in the regime where there is a one-parameter family of nontrivial invariant measures. For these systems there are naturally defined corresponding finite systems, {Mathematical expression}, with {Mathematical expression}. Our main result gives a comparison between the laws of x(t N ) and x N (t N ) for times t N →∞ as N→∞. The comparison involves certain mixtures of the invariant measures for the infinite system.

Original languageEnglish (US)
Pages (from-to)165-197
Number of pages33
JournalProbability Theory and Related Fields
Volume103
Issue number2
DOIs
StatePublished - Jun 1 1995

Keywords

  • Mathematics Subject Classification (1991): 60K35

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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