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

Endre CsákiMiklós CsörgőAntónia FöldesPál Révész — 2009

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

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.

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