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

Michał Morayne () and Krzysztof Tabisz ()
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Michał Morayne: Wrocław University of Technology
Krzysztof Tabisz: Wrocław University

Journal of Theoretical Probability, 2008, vol. 21, issue 1, 1-13

Abstract: Abstract We consider filtrations for which all ℋ2 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.

Keywords: Martingale; Integrable variation; Filtration; Metric; Sigma-algebra; 60G44; 62B10 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0131-9

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