A quasimartingale characterization of p stable type Banach spaces

Florian Hechner (1) , Bernard Heinkel (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We characterize Banach spaces B of stable type p (1 < p < 2) by the property that for every sequence (X_i) of B-valued random variables, independent, centered and fulfilling some integrability assumption, the sequence S_n/n^(1/p) is a quasimartingale, where S_n=X_1+...+X_n.

Mots clés: Marcinkiewicz-Zygmund Law of Large Numbers; Quasimartingales; Rademacher type of a Banach space; Stable type of a Banach space

Domaines: Probabilités [math.PR]

Florian Hechner, Bernard Heinkel. A quasimartingale characterization of p stable type Banach spaces. 2010. ⟨hal-00490272⟩