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A Brief Introduction to Large Deviations Theory

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Stochastic Biomathematical Models

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2058))

Abstract

In this chapter we introduce the main concepts of large deviations theory. We state some of the main theorems with several examples, from Cramér theorem for the sum of independent random variables, to Freidlin–Wentzell theory of random perturbation of dynamical systems.

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Authors and Affiliations

  1. Laboratoire Analyse Géométrie et Applications, Institut Galilée, Université Paris 13, Villetaneuse, France

    Gilles Wainrib

Authors
  1. Gilles Wainrib
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Correspondence to Gilles Wainrib .

Editor information

Editors and Affiliations

  1. College of Sciences, Department of Mathematics, King Saud University, King Khalid Road, Diriyah Campus, Riyadh, 11451, Saudi Arabia

    Mostafa Bachar

  2. Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Jerry Batzel

  3. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark

    Susanne Ditlevsen

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Wainrib, G. (2013). A Brief Introduction to Large Deviations Theory. In: Bachar, M., Batzel, J., Ditlevsen, S. (eds) Stochastic Biomathematical Models. Lecture Notes in Mathematics(), vol 2058. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32157-3_3

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