Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales |
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Authors: | Ashkan Nikeghbali |
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Institution: | (1) Departement Mathematik, ETH Zurich, HG G16, Ramistrasse 101, 8092 Zurich, Switzerland |
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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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Keywords: | random times submartingales general theory of stochastic processes |
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