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Super-Brownian motion with reflecting historical paths
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  • Published: December 2001

Super-Brownian motion with reflecting historical paths

  • Krzysztof Burdzy1 &
  • Jean-François Le Gall2 

Probability Theory and Related Fields volume 121, pages 447–491 (2001)Cite this article

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  • 3 Citations

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Abstract.

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In particular, we show that for any γ > 0, a “typical” increment of a reflecting historical path over a small time interval Δt is not greater than (Δt)3/4−γ.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA. e-mail: burdzy@math.washington.edu, , , , , , US

    Krzysztof Burdzy

  2. DMA – Ecole Normale Supérieure, 45, rue dUlm, 75230 Paris Cedex 05, France. e-mail: legall@dma.ens.fr, , , , , , FR

    Jean-François Le Gall

Authors
  1. Krzysztof Burdzy
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  2. Jean-François Le Gall
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Additional information

Received: 16 March 2000 / Revised version: 26 February 2001 / Published online: 9 October 2001

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Burdzy, K., Le Gall, JF. Super-Brownian motion with reflecting historical paths. Probab Theory Relat Fields 121, 447–491 (2001). https://doi.org/10.1007/s004400100157

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  • Issue Date: December 2001

  • DOI: https://doi.org/10.1007/s004400100157

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Keywords

  • Small Time
  • Limit Distribution
  • Discrete Approximation
  • Historical Path
  • Path Behavior
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