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Excursion theory for Brownian motion indexed by the Brownian tree · Around

2015

Excursion theory for Brownian motion indexed by the Brownian tree

Abraham, Céline, Gall, Jean-François Le

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We develop an excursion theory for Brownian motion indexed by the Brownian tree, which in many respects is analogous to the classical It\^o theory for linear Brownian motion.

Each excursion is associated with a connected component of the complement of the zero set of the tree-indexed Brownian motion.
Each such connectedcomponent is itself a continuous tree, and we introduce a quantity measuring the length of its boundary.
The collection of boundary lengths coincides with the collection of jumps of a continuous-state branching process with branching mechanism $\psi(u)=\sqrt{8/3}\,u^{3/2}$.

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1993
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1995
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Derbez, E., Slade, G
1998
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