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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Vector-valued stochastic processes. V. Optional and predictable variation of stochastic measures and stochastic processes


Author: Nicolae Dinculeanu
Journal: Proc. Amer. Math. Soc. 104 (1988), 625-631
MSC: Primary 60G07; Secondary 60G57
MathSciNet review: 962839
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Abstract: Let $ \mu $ be a stochastic measure, with values in a Banach space $ E$, with finite variation $ \vert\mu \vert$. If $ \mu $ is optional (resp. predictable), then $ \vert\mu \vert$ is also optional (resp. predictable) provided $ E$ is separable, or the dual of a separable space, or has the Radon-Nikodym property.

Let $ A$ be a right continuous stochastic process with values in $ E$, with finite variation $ \vert A\vert$. If $ A$ is measurable (resp. optional, predictable), then $ \vert A\vert$, the continuous part $ \vert A{\vert^c}$ and the discrete part $ \vert A{\vert^d}$ have the same property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0962839-8
PII: S 0002-9939(1988)0962839-8
Keywords: Stochastic processes, stochastic measures, finite variation, measurable, optional, predictable, Banach space
Article copyright: © Copyright 1988 American Mathematical Society