Filtrations for which All ℋ2 Martingales Are of Integrable Variation; Distances between σ-Algebras

We consider filtrations for which all ℋ 2 martingales are of integrable variation. We find a sufficient condition and a necessary condition for this property. Both these conditions are stated in terms the volume of a filtration. The volume of a filtration is defined using a metric on a space of σ -a...

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Bibliographic Details
Published in:	Journal of theoretical probability Vol. 21; no. 1; pp. 1 - 13
Main Authors:	Morayne, Michał, Tabisz, Krzysztof
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01-03-2008
Subjects:	Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Statistics 60G44 Filtration Integrable variation 62B10 Sigma-algebra Martingale Metric
Online Access:	Get full text
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Summary:	We consider filtrations for which all ℋ 2 martingales are of integrable variation. We find a sufficient condition and a necessary condition for this property. Both these conditions are stated in terms the volume of a filtration. The volume of a filtration is defined using a metric on a space of σ -algebras. To obtain the aforementioned conditions we use two equivalent metrics introduced by Boylan and Rogge. We also prove that the original definitions of these metrics can be simplified.
ISSN:	0894-9840 1572-9230
DOI:	10.1007/s10959-007-0131-9