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

Dinculeanu, Nicolae

doi:10.1090/S0002-9939-1988-0962839-8

Vector-valued stochastic processes. V. Optional and predictable variation of stochastic measures and stochastic processes
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by Nicolae Dinculeanu PDF

Proc. Amer. Math. Soc. 104 (1988), 625-631 Request permission

Abstract:

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

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