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On some properties of universal sigma-finite measures associated with a remarkable class of submartingales


Najnudel, Joseph; Nikeghbali, Ashkan (2011). On some properties of universal sigma-finite measures associated with a remarkable class of submartingales. Publications of the Research Institute for Mathematical Sciences, 47(4):911-936.

Abstract

In a previous work, we associated with any submartingale X of class (Sigma), defined on a filtered probability space (Omega, F, (F-t)(t >= 0), P) satisfying some technical conditions, a sigma-finite measure Q on (Omega, F) such that for all t >= 0, and for all events Lambda(t) is an element of F-t, Q[Λt,g≤t]=EP[1ΛtXt], where g is the last hitting time of zero by the process X. In this paper we establish some remarkable properties of this measure from which we also deduce a universal class of penalisation results of the probability measure P with respect to a large class of functionals. The measure Q appears to be the unifying object in these problems.

Abstract

In a previous work, we associated with any submartingale X of class (Sigma), defined on a filtered probability space (Omega, F, (F-t)(t >= 0), P) satisfying some technical conditions, a sigma-finite measure Q on (Omega, F) such that for all t >= 0, and for all events Lambda(t) is an element of F-t, Q[Λt,g≤t]=EP[1ΛtXt], where g is the last hitting time of zero by the process X. In this paper we establish some remarkable properties of this measure from which we also deduce a universal class of penalisation results of the probability measure P with respect to a large class of functionals. The measure Q appears to be the unifying object in these problems.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:December 2011
Deposited On:14 Mar 2013 07:11
Last Modified:07 Dec 2017 18:24
Publisher:European Mathematical Society
ISSN:0034-5318
Publisher DOI:https://doi.org/10.2977/PRIMS/56

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