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Stopping a two parameter weak martingale
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  • Published: December 1987

Stopping a two parameter weak martingale

  • Ely Merzbach1 &
  • Moshe Zakai2 

Probability Theory and Related Fields volume 76, pages 499–507 (1987)Cite this article

  • 78 Accesses

  • 4 Citations

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Summary

This paper deals with the following problem, given a two parameter stochastic process, under what conditions is it possible to stop the process at any stopping line? It is shown that the class of stoppable processes is strictly larger than the class of two parameter integrators. Sufficient conditions for a weak martingale to be stoppable are derived and the stopped r.v. is represented as a one parameter optional dual projection.

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References

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, Bar-Ilan University, 52100, Ramat-Gan, Israel

    Ely Merzbach

  2. Dept. of Electrical Engineering, Technion, Israel Inst. of Technology, 3200, Haifa, Israel

    Moshe Zakai

Authors
  1. Ely Merzbach
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  2. Moshe Zakai
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Additional information

Work partially supported by a grant from the Research Authority at Bar-Ilan University

Work supported by the fund for promotion of research at the Technion

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Cite this article

Merzbach, E., Zakai, M. Stopping a two parameter weak martingale. Probab. Th. Rel. Fields 76, 499–507 (1987). https://doi.org/10.1007/BF00960070

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  • Received: 03 March 1986

  • Issue Date: December 1987

  • DOI: https://doi.org/10.1007/BF00960070

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Parameter Integrator
  • Stoppable Process
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