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

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Listed:
  • Michał Morayne

    (Wrocław University of Technology)

  • Krzysztof Tabisz

    (Wrocław University)

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.

Suggested Citation

  • Michał Morayne & Krzysztof Tabisz, 2008. "Filtrations for which All ℋ2 Martingales Are of Integrable Variation; Distances between σ-Algebras," Journal of Theoretical Probability, Springer, vol. 21(1), pages 1-13, March.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:1:d:10.1007_s10959-007-0131-9
    DOI: 10.1007/s10959-007-0131-9
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    References listed on IDEAS

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    1. Keith F. Taylor & Xikui Wang, 1993. "A metric space associated with probability space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-6, January.
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