Publication date
December 1988
DOI Publisher
Published by Elsevier B.V. ISSN
0304-4149 Citation count (estimate)
19Abstract
AbstractThe first problem attacked in this paper is answering the question whether all 1/α-self-similar α-stable processes with stationary increments are α-stable motions. The answer is yes for α = 2, no for 1⩽α<2 and unknown for 0<α<1. We single out the log-fractional stable processes for 1<α⩽2, different from α-stable motions for α≠2. They can be regarded as the limit of fractional stable processes as the exponent in the kernel tends to 0. The paper ends with a limit theorem for partial sum processes of moving averages of iid random variables in the domain of attraction of a strictly stable law, with log-fractional stable processes as limits in law. The conditions involve de Haan's class Π of slowly varying functions
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