Branching properties of Brownian paths and trees
The authors present the construction of an infinite tree structure associated to a Brownian excursion. The construction is inspired by the results of \textit{J.-F. Le Gall} [in: Séminaire de probabilités XXIII, Lect. Notes Math. 1372, 258-274 (1989; Zbl 0741.60078)], \textit{J. Neveu} and \textit{J.W. Pitman} [ibid., 248-257 (1989; Zbl 0741.60081)], \textit{J.-F. Le Gall} [Ann. Probab. 19, No. 4, 1399-1439 (1991; Zbl 0753.60078)] and \textit{R. Abraham} [in: Séminaire de probabilités XXVI, Lect. Notes Math. 1526, 374-397 (1992; Zbl 0763.60035)]. The same work is done for a reflected Brownian motion perturbed by its local time. These constructions are used to derive an alternative proof of the generalized Ray-Knight theorem.
scientific article; zbMATH DE number 1151669