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2006 Doob's maximal identity, multiplicative decompositions and enlargements of filtrations
Ashkan Nikeghbali, Marc Yor
Illinois J. Math. 50(1-4): 791-814 (2006). DOI: 10.1215/ijm/1258059492

Abstract

In 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.

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Ashkan Nikeghbali. Marc Yor. "Doob's maximal identity, multiplicative decompositions and enlargements of filtrations." Illinois J. Math. 50 (1-4) 791 - 814, 2006. https://doi.org/10.1215/ijm/1258059492

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1101.60059
MathSciNet: MR2247846
Digital Object Identifier: 10.1215/ijm/1258059492

Subjects:
Primary: 60G44
Secondary: 60G40, 60G48

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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