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

AbstractA 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 Rd (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