A canonical setting and separating times for continuous local martingales

The notion of a separating time for a pair of measures on a filtered space is helpful for studying problems of (local) absolute continuity and singularity of measures. In this paper, we describe a certain canonical setting for continuous local martingales (abbreviated below as CLMs) and find an expl...

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Bibliographic Details
Published in:Stochastic processes and their applications 2009-04, Vol.119 (4), p.1039-1054
Main Authors: Engelbert, H.-J., Urusov, M.A., Walther, M.
Format: Article
Language:English
Subjects:
Absolute continuity and singularity
Brownian motion
Canonical setting
Continuous local martingales
Continuous local martingales Brownian motion Dambis-Dubins-Schwarz theorem Canonical setting Pure continuous local martingales Absolute continuity and singularity Separating times
Dambis–Dubins–Schwarz theorem
Exact sciences and technology
Markov processes
Mathematics
Probability and statistics
Probability theory and stochastic processes
Pure continuous local martingales
Sciences and techniques of general use
Separating times
Stochastic analysis
Stochastic processes
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Summary:The notion of a separating time for a pair of measures on a filtered space is helpful for studying problems of (local) absolute continuity and singularity of measures. In this paper, we describe a certain canonical setting for continuous local martingales (abbreviated below as CLMs) and find an explicit form of separating times for CLMs in this setting.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2008.05.003