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Brownian motion on the continuum tree
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  • Published: September 1995

Brownian motion on the continuum tree

  • W. B. Krebs1 

Probability Theory and Related Fields volume 101, pages 421–433 (1995)Cite this article

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Summary

We construct Brownian motion on a continuum tree, a structure introduced as an asymptotic limit to certain families of finite trees. We approximate the Dirichlet form of Brownian motion on the continuum tree by adjoining one-dimensional Brownian excursions. We study the local times of the resulting diffusion. Using time-change methods, we find explicit expressions for certain hitting probabilities and the mean occupation density of the process.

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Authors and Affiliations

  1. Department of Statistics, Florida State University, 32306-3303, Tallahassee, Florida, USA

    W. B. Krebs

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  1. W. B. Krebs
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Krebs, W.B. Brownian motion on the continuum tree. Probab. Th. Rel. Fields 101, 421–433 (1995). https://doi.org/10.1007/BF01200505

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  • Received: 26 August 1994

  • Revised: 28 September 1994

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01200505

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Mathematics Subject Classification

  • 60J65
  • 31C25
  • 60J55
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