The Annals of Probability

Synonymity, Generalized Martingales, and Subfiltration

Douglas N. Hoover

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Abstract

Aldous recently introduced the notion of synonymity of stochastic processes, a notion of equivalence for processes on a stochastic basis which generalizes the notion of "having the same distribution". We show that generalized martingale properties, such as the semimartingale property, are preserved under synonymity, and that synonymous semimartingales have decompositions with the same distribution law. A variation of our method yields a relatively elementary proof of the theorem of Stricker that semimartingale remains a semimartingale with respect to any subfiltration to which it is adapted.

Article information

Source
Ann. Probab. Volume 12, Number 3 (1984), 703-713.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176993221

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176993221

Mathematical Reviews number (MathSciNet)
MR744227

Subjects
Primary: 60G07: General theory of processes
Secondary: 60G48: Generalizations of martingales

Keywords
Synonymity semimartingale local martingale subfiltration

Citation

Hoover, Douglas N. Synonymity, Generalized Martingales, and Subfiltration. Ann. Probab. 12 (1984), no. 3, 703--713. doi:10.1214/aop/1176993221. http://projecteuclid.org/euclid.aop/1176993221.


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