# Rh/Fragment 182 09

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Seite: 182, Zeilen: 9-15
Quelle: Wendin 2004
Seite(n): 10, 11, Zeilen: 36-39; 1-3
The characterization of multivariate regular variation in (6.3.1) is referred to as the sequential definition of regular variation (see Embrechts et al. (1997)) and it describes dependence among the marginals, while (6.3.2) rules out tails that are not regular varying. It is interesting to note that whereas univariate regular variation has been introduced as a function property, all the characterizations of multivariate regular variation are in terms of measures. Multivariate distribution functions are de facto more difficult to deal with than univariate distribution functions and therefore measures appear more natural. The characterization of multivariate regular variation in (ii) is referred to as the sequential definition of regular variation or the Feller definition of regular variation*. It is interesting to note that whereas univariate regular variation has been introduced as a function property, both characterizations of multivariate regular

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variation in Theorem 1.1 are in terms of measures. Multivariate distribution functions are de facto more difficult to deal with than univariate distribution functions and therefore measures appear more natural.

• See Section VIII.8 of Feller vol II [10].
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