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Integrals and derivatives of regularly varying functions in d and domains of attraction of stable distributions II

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  • de Haan, L.
  • Omey, E.

Abstract

A theorem on regularly varying functions in 2 is proved and applied to domains of attraction of stable laws with index 1 [less-than-or-equals, slant] [alpha] [less-than-or-equals, slant] 2. We also present a theory of [Pi]-variation in 2. Unlike the situation in 1 the latter is not connected with domain of attraction theory. The situation in d (d > 1) is more complicated but not essentially different; for simplicity we limit ourselves to 2. This article complements de Haan and Resnick (1979) where the situation for 0

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  • de Haan, L. & Omey, E., 1984. "Integrals and derivatives of regularly varying functions in d and domains of attraction of stable distributions II," Stochastic Processes and their Applications, Elsevier, vol. 16(2), pages 157-170, February.
    • Handle: RePEc:eee:spapps:v:16:y:1984:i:2:p:157-170
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    Cited by:

    1. Li, Haijun & Hua, Lei, 2015. "Higher order tail densities of copulas and hidden regular variation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 143-155.
    2. Tiandong Wang & Sidney I. Resnick, 2018. "Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 1029-1042, September.

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