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

Endre Csáki; Miklós Csörgő; Antónia Földes; Pál Révész

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 2, page 515-544
  • ISSN: 0246-0203

Abstract

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Let ξ(k, n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process ξ(k, n)−ξ(0, n) 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.

How to cite

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Csáki, Endre, et al. "Random walk local time approximated by a brownian sheet combined with an independent brownian motion." Annales de l'I.H.P. Probabilités et statistiques 45.2 (2009): 515-544. <http://eudml.org/doc/78032>.

@article{Csáki2009,
abstract = {Let ξ(k, n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process ξ(k, n)−ξ(0, n) 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.},
author = {Csáki, Endre, Csörgő, Miklós, Földes, Antónia, Révész, Pál},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {local time; random walk; brownian sheet; strong approximation; Brownian sheet},
language = {eng},
number = {2},
pages = {515-544},
publisher = {Gauthier-Villars},
title = {Random walk local time approximated by a brownian sheet combined with an independent brownian motion},
url = {http://eudml.org/doc/78032},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Csáki, Endre
AU - Csörgő, Miklós
AU - Földes, Antónia
AU - Révész, Pál
TI - Random walk local time approximated by a brownian sheet combined with an independent brownian motion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 2
SP - 515
EP - 544
AB - Let ξ(k, n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process ξ(k, n)−ξ(0, n) 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.
LA - eng
KW - local time; random walk; brownian sheet; strong approximation; Brownian sheet
UR - http://eudml.org/doc/78032
ER -

References

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