A Fermion Lévy theorem
type: Item
instance of: scholarly article
title: A Fermion Lévy theorem
zbMATH Open document ID: 0770.60050
DOI: 10.1016/0022-1236(92)90045-K
author: L. Accardi
author: Johan Quaegebeur
published in: Journal of Functional Analysis
publication date: 1993-06-29T00:00:00Z
review text: Lévy's theorem in classical probability theory asserts that any martingale \((M_ t)\), with \(M_ 0=0\), continuous sample paths and such that \(M^ 2_ t-t\) is a martingale, has the same law as standard Brownian motion from 0. The problem is to extend such a theorem to non- commutative probability. One of the main difficulties is to translate the path continuity condition, which the authors interpret as the identity of two natural quadratic variation processes, a ``square bracket'' and an ``angle bracket''. Using this idea, the authors are able to prove a Lévy theorem characterizing Fermion Brownian motion, under an auxiliary hypothesis on the existence of fourth order moments.
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 81S25
zbMATH DE Number: 220680
zbMATH Keywords: quantum martingale
zbMATH Keywords: anticommutation relation
zbMATH Keywords: martingale
zbMATH Keywords: non-commutative probability
zbMATH Keywords: Lévy theorem characterizing Fermion Brownian motion
reviewed by: Paul-André Meyer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 220680