Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion
Jacques Neveu, Jim Pitman (1989)
Séminaire de probabilités de Strasbourg
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Jacques Neveu, Jim Pitman (1989)
Séminaire de probabilités de Strasbourg
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C. M. Newman, K. Ravishankar, E. Schertzer (2010)
Annales de l'I.H.P. Probabilités et statistiques
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The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits...
Gerónimo Uribe Bravo (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We present a further analysis of the fragmentation at heights of the normalized brownian excursion. Specifically we study a representation for the mass of a tagged fragment in terms of a Doob transformation of the 1/2-stable subordinator and use it to study its jumps; this accounts for a description of how a typical fragment falls apart. These results carry over to the height fragmentation of the stable tree. Additionally, the sizes of the fragments in the brownian height fragmentation...
David G. Hobson (2000)
Séminaire de probabilités de Strasbourg
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Abraham, Romain, Werner, Wendelin (1997)
Electronic Journal of Probability [electronic only]
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Itai Benjamini, Nathanaël Berestycki (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We study a one-dimensional brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function (), ≥0, consider the measures obtained by conditioning a brownian path so that ≤(), for all ≤, where is the local time spent at the origin by time . It is shown that the measures are tight, and that any weak limit of as →∞ is transient provided that −3/2() is integrable. We conjecture...
Jacques Neveu, James W. Pitman (1989)
Séminaire de probabilités de Strasbourg
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