Sojourn times for the Brownian motion.
Takács, Lajos (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Takács, Lajos (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Frank B. Knight (1993)
Séminaire de probabilités de Strasbourg
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Davis, Burgess (1998)
The New York Journal of Mathematics [electronic only]
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Cristian Coletti, Glauco Valle (2014)
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.
Jim Pitman (1999)
Séminaire de probabilités de Strasbourg
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Itai Benjamini, Nathanaël Berestycki (2010)
Journal of the European Mathematical Society
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We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show...
Bertoin, Jean, Chaumont, Loïc, Pitman, Jim (2003)
Electronic Communications in Probability [electronic only]
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Neil O'Connell (2002)
Séminaire de probabilités de Strasbourg
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Gittenberger, Bernhard, Louchard, Guy (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Janson, Svante, Chassaing, Philippe (2004)
Electronic Communications in Probability [electronic only]
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Puckette, Emily E., Werner, Wendelin (1996)
Electronic Communications in Probability [electronic only]
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Sznitman, Alain-Sol (1998)
Documenta Mathematica
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Chigansky, Pavel, Klebaner, Fima C. (2008)
Electronic Communications in Probability [electronic only]
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