Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion
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Jacques Neveu, Jim Pitman (1989)
Séminaire de probabilités de Strasbourg
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Takács, Lajos (1995)
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David G. Hobson (2000)
Séminaire de probabilités de Strasbourg
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Séminaire de probabilités de Strasbourg
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Bertoin, Jean, Chaumont, Loïc, Pitman, Jim (2003)
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Gittenberger, Bernhard, Louchard, Guy (2000)
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Aldous, David J. (1998)
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Jean-François Le Gall, Mathilde Weill (2006)
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Annales de l'I.H.P. Probabilités et statistiques
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We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing paths that can cross each other and are dependent even before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.