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Large Deviations for Interacting Processes in the Strong Topology

In: Statistical Modeling and Analysis for Complex Data Problems

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  • Donald A. Dawson
  • Pierre Del Moral

Abstract

Strong large deviations principles for a general class of discrete generation and interacting particle systems are developed. The analysis is essentially conducted through an original projective interpretation of the τ-topology, combined with a powerful projective transfer result presented by the first author with J. Gärtner. These large deviations principles simplify and encompass the ones obtained in an earlier joint work of the second author with A. Guionnet. They are illustrated with simplified versions of McKean-Vlasov diffusions, and Boltzmann type collision models. We also describe the impact of this analysis on a recently developed class of genealogical and interacting particle interpretations of non linear Feynman-Kac-Schrödinger path measures.

Suggested Citation

  • Donald A. Dawson & Pierre Del Moral, 2005. "Large Deviations for Interacting Processes in the Strong Topology," Springer Books, in: Pierre Duchesne & Bruno RÉMillard (ed.), Statistical Modeling and Analysis for Complex Data Problems, chapter 0, pages 179-208, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-24555-3_10
    DOI: 10.1007/0-387-24555-3_10
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