Shortest excursion lengths
Yueyun Hu, Zhan Shi (1999)
Annales de l'I.H.P. Probabilités et statistiques
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Yueyun Hu, Zhan Shi (1999)
Annales de l'I.H.P. Probabilités et statistiques
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Annales de l'I.H.P. Probabilités et statistiques
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Annales de l'I.H.P. Probabilités et statistiques
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Acta Arithmetica
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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.