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Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales

Nikeghbali, Ashkan

In: Journal of Theoretical Probability, 2006, vol. 19, no. 4, p. 931-949

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    Titre
    • Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales
    Auteur
    • Nikeghbali, Ashkan. Departement Mathematik, ETH Zurich, HG G16, Ramistrasse 101, 8092, Zurich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Theoretical Probability, 2006, vol. 19, no. 4, p. 931-949. Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:322319
    Summary
    In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y=N+A, where the measure dA is carried by the set of zeros of Y. In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, these submartingales are the smallest ones. We also study some integrability questions in the multiplicative decomposition and interpret the notion of saturated sets in the light of our results