Large-Deviation Principles

  • Pierre Del Moral
Part of the Probability and its Applications book series (PIA)


This chapter focuses on large-deviation principles for interacting particle models. The main object of the theory of large deviations is to provide sharp exponential estimates of the deviant behavior of random rare events. For instance, in the context of interacting particle models, these events represent the deviations of particle approximation measures around the “nondeviant” limiting McKean distribution or around the solution of the Umiting measure-valued equation. We have already analyzed some rather crude exponential decays of these deviation probabilities in Section 7.4. Although these estimates were not asymptotic, they were far from being sharp. These exponential decays are sometimes called strong large-deviation estimates by some authors. In this context, a large-deviation analysis will provide sharp and precise estimates. Before entering into more details on this subject, it is useful to give some comments on the origins of the theory of large deviations and its connections with other scientific disciplines.


Weak Topology Projective Limit Hausdorff Topological Space Good Rate Function Idempotent Analysis 
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Copyright information

© Springer-Verlag New York, LLC 2004

Authors and Affiliations

  • Pierre Del Moral
    • 1
  1. 1.Laboratoire de Statistique et ProbabilitésUniversité Paul SabatierToulouse, Cedex 4France

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