The well-known concept of conjugate slowly varying functions is specialized to the subclass $\Pi$ of the slowly varying functions. The concept is then used to connect convergence of certain increasing stochastic processes (suitably normalized) with convergence of their inverses.
Publié le : 1979-12-14
Classification:
$\Pi$-variation,
conjugate transformation,
regular variation,
weak convergence,
$M_1$ and $J_1$ topology,
first passage processes,
renewal processes,
extremal process,
60F05,
60B10
@article{1176994895,
author = {de Haan, L. and Resnick, S. I.},
title = {Conjugate $\Pi$-Variation and Process Inversion},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 1028-1035},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994895}
}
de Haan, L.; Resnick, S. I. Conjugate $\Pi$-Variation and Process Inversion. Ann. Probab., Tome 7 (1979) no. 6, pp. 1028-1035. http://gdmltest.u-ga.fr/item/1176994895/