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Super-Brownian motion with reflecting historical paths. II. Convergence of approximations
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  • Published: 10 February 2005

Super-Brownian motion with reflecting historical paths. II. Convergence of approximations

  • Krzysztof Burdzy1 &
  • Leonid Mytnik2 

Probability Theory and Related Fields volume 133, pages 145–174 (2005)Cite this article

Abstract.

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the “super-Brownian motion with reflecting historical paths.” This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits–they obviously hold for the unique limit found in the present paper.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, 354350, Seattle, WA 98115-4350, USA

    Krzysztof Burdzy

  2. Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, Haifa, 32000, Israel

    Leonid Mytnik

Authors
  1. Krzysztof Burdzy
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  2. Leonid Mytnik
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Corresponding author

Correspondence to Krzysztof Burdzy.

Additional information

Mathematics Subject Classification (2000): Primary 60H15, Secondary 35R60

Supported in part by NSF Grant DMS-0071486, Israel Science Foundation Grants 12/98 and 116/01 - 10.0, and the U.S.-Israel Binational Science Foundation (grant No. 2000065).

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Burdzy, K., Mytnik, L. Super-Brownian motion with reflecting historical paths. II. Convergence of approximations. Probab. Theory Relat. Fields 133, 145–174 (2005). https://doi.org/10.1007/s00440-004-0413-4

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  • Received: 09 September 2002

  • Revised: 31 October 2004

  • Published: 10 February 2005

  • Issue Date: October 2005

  • DOI: https://doi.org/10.1007/s00440-004-0413-4

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Keywords

  • Super-Brownian motion
  • Reflecting paths
  • Brownian snake
  • Martingale problem
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