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April 1996 $\epsilon$-close measures producing nonisomorphic filtrations
J. Feldman
Ann. Probab. 24(2): 912-915 (April 1996). DOI: 10.1214/aop/1039639369

Abstract

A consequence of the preceding two papers is this. Let $\{\mathscr{A}_t: 0 \leq t < \infty\}$ be the filtration of a stochastic process on $(\Omega, \mathscr{A},P)$. Under a mild assumption on the process, there exist, for any $\varepsilon > 0$, uncountably many probability measures $Q_\alpha$ with $(1 - \varepsilon) P \leq Q_\alpha \leq (1+ \varepsilon)P$ so that no two of the filtrations $(\Omega, (\mathscr{A}_t)_{o \leq t}, Q_\alpha)$ and $(\Omega (\mathscr{A}_t)_{o\leq t}, Q_\beta), \alpha \not= \beta$, can be generated by equivalent stochastic processes.

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J. Feldman. "$\epsilon$-close measures producing nonisomorphic filtrations." Ann. Probab. 24 (2) 912 - 915, April 1996. https://doi.org/10.1214/aop/1039639369

Information

Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0879.60077
MathSciNet: MR1404535
Digital Object Identifier: 10.1214/aop/1039639369

Subjects:
Primary: 60G07

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 2 • April 1996
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