Two classes of processes are considered. One is a class of
spectrally positive infinitely divisible processes which includes all such
stable processes. The other is a class of processes constructed from the
sequence of partial sums of independent identically distributed positive random
variables. A condition analogous to regular variation of the tails is imposed.
Then a large deviation principle and a Strassen-type law of the iterated
logarithm are presented. These theorems focus on unusually large values of the
processes. They are expressed in terms of Skorokhod’s $M_1$
topology.
Publié le : 1999-04-15
Classification:
Spectrally positive,
stable processes,
infinitely divisible,
partial sums,
large deviations,
law of the interated logarithm,
the $M_1$ topology,
60F10,
60F20,
60G50
@article{1022677393,
author = {O'Brien, George L.},
title = {Unusually Large Values for Spectrally Positive Stable and Related
Processes},
journal = {Ann. Probab.},
volume = {27},
number = {1},
year = {1999},
pages = { 990-1008},
language = {en},
url = {http://dml.mathdoc.fr/item/1022677393}
}
O’Brien, George L. Unusually Large Values for Spectrally Positive Stable and Related
Processes. Ann. Probab., Tome 27 (1999) no. 1, pp. 990-1008. http://gdmltest.u-ga.fr/item/1022677393/