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Derivatives of regularly varying functions in Rd and domains of attraction of stable distributions

Author

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  • de Haan, L.
  • Resnick, S. I.

Abstract

In R2 the integral of a regularly varying (RV) function f is regularly varying only if f is monotone. Generalization to R2 of the one-dimensional result on regular variation of the derivative of an RV-function however is straightforward. Applications are given to limit theory for partial sums of i.i.d. positive random vectors in R2+.

Suggested Citation

  • de Haan, L. & Resnick, S. I., 1979. "Derivatives of regularly varying functions in Rd and domains of attraction of stable distributions," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 349-355, May.
  • Handle: RePEc:eee:spapps:v:8:y:1979:i:3:p:349-355
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    Cited by:

    1. Yi He & John H. J. Einmahl, 2017. "Estimation of extreme depth-based quantile regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 449-461, March.
    2. Asimit, Alexandru V. & Gerrard, Russell & Hou, Yanxi & Peng, Liang, 2016. "Tail dependence measure for examining financial extreme co-movements," Journal of Econometrics, Elsevier, vol. 194(2), pages 330-348.
    3. Dermoune, A. & Hamadène, S. & Ouknine, Y., 1999. "Limit theorem for the statistical solution of Burgers equation," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 217-230, June.

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