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Multiplicative decompositions and frequency of vanishing of nonnegative submartingales


Nikeghbali, A (2006). Multiplicative decompositions and frequency of vanishing of nonnegative submartingales. Journal of Theoretical Probability, 19(4):931-949.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:random times - submartingales - general theory of stochastic processes
Language:English
Date:2006
Deposited On:20 Jan 2010 10:57
Last Modified:19 Feb 2018 06:50
Publisher:Springer
ISSN:0894-9840
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s10959-006-0035-0
Related URLs:http://arxiv.org/abs/math/0506369

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Content: Accepted Version
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Size: 185kB