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

Abstract:

A theorem on regularly varying functions in R² is proved and applied to domains of attraction of stable laws with index 1 ≤ α ≤ 2. We also present a theory of Π-variation in R². Unlike the situation in R¹ the latter is not connected with domain of attraction theory. The situation in R^d (d > 1) is more complicated but not essentially different; for simplicity we limit ourselves to R². This article complements de Haan and Resnick (1979) where the situation for 0 < α < 1 was considered. © 1983.

Año de publicación:

1984

Keywords:

Fuente:

scopus