We determine: (a) the joint almost sure asymptotic behaviour of the most visited site and the maximum local time of a one-dimensional simple random walk or Brownian motion; (b) the maximal jump size of the most visited site. In so doing, we solve two open problems of Erdös and Révész.
Publié le : 2000-12-14
Classification:
Brownian motion,
favourite site,
local time,
random walk
@article{1081194154,
author = {Cs\'aki,, Endre and R\'ev\'esz, P\'al and Shi, Zhan},
title = {Favourite sites, favourite values and jump sizes for random walk and Brownian motion},
journal = {Bernoulli},
volume = {6},
number = {6},
year = {2000},
pages = { 951-975},
language = {en},
url = {http://dml.mathdoc.fr/item/1081194154}
}
Csáki,, Endre; Révész, Pál; Shi, Zhan. Favourite sites, favourite values and jump sizes for random walk and Brownian motion. Bernoulli, Tome 6 (2000) no. 6, pp. 951-975. http://gdmltest.u-ga.fr/item/1081194154/