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Journal of Theoretical Probability

, Volume 19, Issue 4, pp 931–949 | Cite as

Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales

  • Ashkan Nikeghbali
Article

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.

Keywords

random times submartingales general theory of stochastic processes 

2000 Mathematics Subject Classification

05C38 15A15 05A15 15A18 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Departement MathematikETH ZurichZurichSwitzerland

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