### The Beurling estimate for a class of random walks.

Lawler, Gregory F., Limic, Vlada (2004)

Electronic Journal of Probability [electronic only]

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Lawler, Gregory F., Limic, Vlada (2004)

Electronic Journal of Probability [electronic only]

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Csáki, Endre, Hu, Yueyun (2004)

Electronic Communications in Probability [electronic only]

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Eichelsbacher, Peter, König, Wolfgang (2008)

Electronic Journal of Probability [electronic only]

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Berestycki, Nathanael, Durrett, Rick (2008)

Electronic Journal of Probability [electronic only]

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Holmes, Mark P. (2009)

Electronic Communications in Probability [electronic only]

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Philippe Carmona (2010)

ESAIM: Probability and Statistics

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The sequence of random probability measures that gives a path of length , $\frac{1}{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.

Pak, Igor (1999)

Electronic Journal of Probability [electronic only]

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Guillotin-Plantard, Nadine, Le Ny, Arnaud (2008)

Electronic Communications in Probability [electronic only]

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Merkl, Franz, Rolles, Silke W.W. (2008)

Electronic Journal of Probability [electronic only]

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Endre Csáki, Miklós Csörgő, Antónia Földes, Pál Révész (2009)

Annales de l'I.H.P. Probabilités et statistiques

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Let (, ) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process (, )−(0, ) in terms of a brownian sheet and an independent Wiener process (brownian motion), time changed by an independent brownian local time. Some related results and consequences are also established.

Zakhar Kabluchko, Axel Munk (2009)

ESAIM: Probability and Statistics

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We generalize a theorem of Shao [ (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well...