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A note on the localization of two-parameter processes
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  • Published: March 1986

A note on the localization of two-parameter processes

  • Peter Imkeller1 nAff2 

Probability Theory and Related Fields volume 73, pages 119–125 (1986)Cite this article

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Summary

Continuous two-parameter strong martingalesM andN with respect to a filtration, which is closely related to the filtration of a Wiener sheet, are constructed such thatM and the continuous increasing process [N] ofN (identical with the quadratic variation) cannot be “boundedly localized”: each stopping domainD for which the processesM or [N] stopped byD, are bounded must be contained in a nontrivial subset of ℝ 2+ which only depends onM orN.

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Author notes
  1. Peter Imkeller

    Present address: Mathematisches Institut der Ludwig-Maximilians, Universität München, Theresienstrasse 39, D-8000, München 2, Federal Republic of Germany

Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210, Columbus, OH, USA

    Peter Imkeller

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  1. Peter Imkeller
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Cite this article

Imkeller, P. A note on the localization of two-parameter processes. Probab. Th. Rel. Fields 73, 119–125 (1986). https://doi.org/10.1007/BF01845995

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  • Received: 10 March 1985

  • Revised: 06 January 1986

  • Issue Date: March 1986

  • DOI: https://doi.org/10.1007/BF01845995

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Keywords

  • Filtration
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Quadratic Variation
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