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Brownian motion on the continuum tree. (English) Zbl 0822.60069
The author constructs a so-called Brownian motion on the continuum tree, that is a continuous symmetric Markov process with further special properties of hitting times of points. The elegant construction relies on the theory of Dirichlet forms. Typically, a continuous Markov process \(X^ 0\) is first obtained as the diffusion associated to some regular local Dirichlet form; and then the Brownian motion \(X\) is defined by a time-change of \(X^ 0\) based on an adequate additive functional. Moreover, one can establish the existence of a jointly continuous version of the local times of \(X^ 0\), using recent results of M. B. Marcus and J. Rosen [Ann. Probab. 20, No. 4, 1603-1684 (1992; Zbl 0762.60068)].
Reviewer: J.Bertoin (Paris)

60J65 Brownian motion
31C25 Dirichlet forms
60J55 Local time and additive functionals
Full Text: DOI
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