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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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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DOI: https://doi.org/10.1007/BF01200505
Mathematics Subject Classification
- 60J65
- 31C25
- 60J55