Doob's maximal identity, multiplicative decompositions and enlargements of filtrations

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dc.creatorNikeghbali, A.
dc.creatorYor, M.
dc.date2005-03-18
dc.date2007-08-02
dc.date.accessioned2026-07-07T08:21:57Z
dc.date.available2026-07-07T08:21:57Z
dc.descriptionIn the theory of progressive enlargements of filtrations, the supermartingale $Z_{t}=\mathbf{P}(g>t\mid \mathcal{F}_{t}) $ associated with an honest time g, and its additive (Doob-Meyer) decomposition, play an essential role. In this paper, we propose an alternative approach, using a multiplicative representation for the supermartingale Z_{t}, based on Doob's maximal identity. We thus give new examples of progressive enlargements. Moreover, we give, in our setting, a proof of the decomposition formula for martingales, using initial enlargement techniques, and use it to obtain some path decompositions given the maximum or minimum of some processes.
dc.descriptionTypos corrected
dc.identifierhttps://arxiv.org/abs/math/0503386
dc.identifierhttp://arxiv.org/abs/math/0503386
dc.identifierIllinois Journal of Mathematics, 50 (4), 791-814 (2006)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135494
dc.subjectProbability
dc.subject05C38, 15A15, 05A15, 15A18
dc.titleDoob's maximal identity, multiplicative decompositions and enlargements of filtrations
dc.typetext

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