Lithuanian Mathematical Journal

, Volume 58, Issue 4, pp 384–398 | Cite as

On extremal indices greater than one for a scheme of series

  • Anna A. GoldaevaEmail author
  • Alexey V. Lebedev


The classic extremal index θ is an important parameter of asymptotic behavior of maxima of stationary random sequences. For applications, however, it is interesting to investigatemore complex structures. Recently, the extremal index was generalized to a scheme of series of random length. If the exact extremal index does not exist, then we consider partial indices. In contrast to the classic index, partial indices can be greater than one. In this paper, we consider a new model, where left and right partial indices can be greater than one and equal to each other, although the exact index does not exist.


extremal index scheme of series heavy tails maxima copula 


60G70 62G32 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Probability Theory, Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia

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