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.

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.

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## Additional indexing

Item Type: | Journal Article, not refereed, original work |
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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: | 05 Apr 2016 16:19 |

Publisher: | European Mathematical Society |

ISSN: | 0034-5318 |

Publisher DOI: | https://doi.org/10.2977/PRIMS/56 |

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