Probability Theory and Related Fields

, Volume 101, Issue 3, pp 421–433

Brownian motion on the continuum tree

  • W. B. Krebs

DOI: 10.1007/BF01200505

Cite this article as:
Krebs, W.B. Probab. Th. Rel. Fields (1995) 101: 421. doi:10.1007/BF01200505


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.

Mathematics Subject Classification


Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • W. B. Krebs
    • 1
  1. 1.Department of StatisticsFlorida State UniversityTallahasseeUSA