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On multiplicative excessive functions of a branching Brownian motion
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  • Published: March 1990

On multiplicative excessive functions of a branching Brownian motion

  • Paavo Salminen1 

Probability Theory and Related Fields volume 85, pages 43–56 (1990)Cite this article

Summary

In this note stochastic calculus is used to characterise multiplicative excessive functions of a binary branching Brownian motion with a constant creation rate. Some properties of the martingales given by invariant functions are studied. In particular, it is seen that these positive and unbounded martingales tend a.s. to 0 and are not square integrable. Informally speaking, they exhibit a clustering phenomenon in the underlying supercritical branching Brownian motion.

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Author information

Authors and Affiliations

  1. Åbo Akademi, Mathematical Institute, SF-20500, Åbo, Finland

    Paavo Salminen

Authors
  1. Paavo Salminen
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Additional information

This work was done while the author was visiting the University of British Columbia, Mathematical Department, and was partly supported by a NSERC grant. AMS 1980 subject classifications: primary 60J80, 60J65 secondary 60J60

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Cite this article

Salminen, P. On multiplicative excessive functions of a branching Brownian motion. Probab. Th. Rel. Fields 85, 43–56 (1990). https://doi.org/10.1007/BF01377627

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  • Received: 05 September 1988

  • Revised: 28 August 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01377627

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Mathematical Biology
  • Invariant Function
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