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Displaying similar documents to “Invariance principles for ranked excursion lengths and heights.”

Regularity of irregularities on a brownian path

Samuel James Taylor (1974)

Annales de l'institut Fourier

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On a standard Brownian motion path there are points where the local behaviour is different from the pattern which occurs at a fixed t 0 with probability 1. This paper is a survey of recent results which quantity the extent of the irregularities and show that the exceptional points themselves occur in an extremely regular manner.

Random walk local time approximated by a brownian sheet combined with an independent brownian motion

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.