VI: 03, 51-71, LNM 258 (1972)
BRETAGNOLLE, Jean
$p$-variation de fonctions aléatoires~: 1. Séries de Rademacher 2. Processus à accoissements indépendants (Independent increments)
The main result of the paper is theorem III, which gives a necessary and sufficient condition for the sample paths of a centered Lévy process to have a.s. a finite $p$-variation on finite time intervals, for $1<p<2$: the process should have no Gaussian part, and $|x|^p$ be integrable near $0$ w.r.t. the Lévy measure $L(dx)$. The proof rests on discrete estimates on the $p$-variation of Rademacher series. Additional results on $h$-variation w.r.t. more general convex functions are given or mentioned
Comment: This paper improves on Millar, Zeit. für W-theorie, 17, 1971
Keywords: $p$-variation, Rademacher functions
Nature: Original
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