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Derivatives of regularly varying functions in Rd and domains of attraction of stable distributions |
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| Authors: | L de Haan SI Resnick |
| Institution: | Faculteit der Economische Wetenschappen, Erasmus Universiteit, Rotterdam, The Netherlands;Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A. |
| 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+. |
| Keywords: | Multivariate regular variatiion Tauberian theorems multivariate stable laws domains of attraction |
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