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Predictability and stopping on lattices of sets
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  • Published: December 1993

Predictability and stopping on lattices of sets

  • B. Gail Ivanoff1,
  • Ely Merzbach2 &
  • Ioana Şchiopu-Kratina1 

Probability Theory and Related Fields volume 97, pages 433–446 (1993)Cite this article

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Summary

As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable σ-algebra in terms of adapted and “left-continuous” processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable σ-algebra can be characterized by various stochastic intervals generated by stopping sets.

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Authors and Affiliations

  1. Department of Mathematics, University of Ottawa, KIN 6N5, Ottawa, Ontario, Canada

    B. Gail Ivanoff & Ioana Şchiopu-Kratina

  2. Department of Mathematics, Bar-Han University, 52900, Ramat-Gan, Israel

    Ely Merzbach

Authors
  1. B. Gail Ivanoff
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  2. Ely Merzbach
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  3. Ioana Şchiopu-Kratina
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Additional information

Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada

Research partially done while the second author was visiting the University of Ottawa. He wishes to thank the Department of Mathematics for its hospitality

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Ivanoff, B.G., Merzbach, E. & Şchiopu-Kratina, I. Predictability and stopping on lattices of sets. Probab. Th. Rel. Fields 97, 433–446 (1993). https://doi.org/10.1007/BF01192958

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  • Received: 10 March 1992

  • Revised: 07 May 1993

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01192958

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Mathematics Classification (1985)

  • 60G07
  • 60G60
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