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This article is cited in 10 scientific papers (total in 10 papers)
Short Communications
Separating times for measures on filtered spaces
M. A. Urusov, A. S. Cherny M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
We introduce the notion of a separating time for a pair of measures $P$ and $\widetilde{P}$ on a filtered space. This notion is convenient for describing the mutual arrangement of $P$ and $\widetilde{P}$ from the viewpoint of the absolute continuity and singularity.
Furthermore, we find the explicit form of the separating time for the case, where $P$ and $\widetilde{P}$ are distributions of Lévy processes, solutions of stochastic differential equations, and distributions of Bessel processes. The obtained results yield, in particular, the criteria for the local absolute continuity, absolute continuity, and singularity of $P$ and $\widetilde{P}$.
Keywords:
separating time, local absolute continuity, absolute continuity, singularity, Lévy processes, stochastic differential equations, Bessel processes.
Received: 19.03.2003
Citation:
M. A. Urusov, A. S. Cherny, “Separating times for measures on filtered spaces”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 416–427; Theory Probab. Appl., 48:2 (2004), 337–347
Linking options:
https://www.mathnet.ru/eng/tvp296https://doi.org/10.4213/tvp296 https://www.mathnet.ru/eng/tvp/v48/i2/p416
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Abstract page: | 337 | Full-text PDF : | 171 | References: | 69 |
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