Displaying similar documents to “Special points of the Brownian net.”

Marking (1, 2) points of the brownian web and applications

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...

Revisiting the sample path of Brownian motion

S. James Taylor (2006)

Banach Center Publications

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Brownian motion is the most studied of all stochastic processes; it is also the basis for stochastic analysis developed in the second half of the 20th century. The fine properties of the sample path of a Brownian motion have been carefully studied, starting with the fundamental work of Paul Lévy who also considered more general processes with independent increments and extended the Brownian motion results to this class. Lévy showed that a Brownian path in d (d ≥ 2) dimensions had zero...

Hitting probabilities and potential theory for the brownian path-valued process

Jean-François Le Gall (1994)

Annales de l'institut Fourier

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We consider the Brownian path-valued process studied in [LG1], [LG2], which is closely related to super Brownian motion. We obtain several potential-theoretic results related to this process. In particular, we give an explicit description of the capacitary distribution of certain subsets of the path space, such as the set of paths that hit a given closed set. These capacitary distributions are characterized as the laws of solutions of certain stochastic differential equations. They solve...