Densities and Local Probabilities

  • Sergey Foss
  • Dmitry Korshunov
  • Stan Zachary
Chapter
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)

Abstract

This chapter is devoted to local long-tailedness and to local subexponentiality. First we consider densities with respect to either Lebesgue measure on \(\mathbb{R}\) or counting measure on \(\mathbb{Z}\). Next we study the asymptotic behaviour of the probabilities to belong to an interval of a fixed length. We give the analogues of the basic properties of the tail probabilities including two analogues of Kesten’s estimate, and provide sufficient conditions for probability distributions to have these local properties.

Keywords

Covariance Convolution 

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Copyright information

© Springer Science + Business Media New York 2013

Authors and Affiliations

  • Sergey Foss
    • 1
  • Dmitry Korshunov
    • 2
  • Stan Zachary
    • 1
  1. 1.Department of Actuarial MathematicsHeriot-Watt UniversityEdinburghUK
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia

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