Authors
Citation
P. Vallois, THE RANGE OF A SIMPLE RANDOM-WALK ON Z, Advances in Applied Probability, 28(4), 1996, pp. 1014-1033
Citations number
19
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
ISSN journal
00018678
Volume
28
Issue
4
Year of publication
1996
Pages
1014 - 1033
Database
ISI
SICI code
0001-8678(1996)28:4<1014:TROASR>2.0.ZU;2-9
Abstract
Let theta(a) be the first time when the range (R(n); n greater than or
equal to 0) is equal to a, R(n) being equal to the difference of the
maximum and the minimum, taken at time n, of a simple random walk on Z
. We compute the g.f. of theta(a); this allows us to compute the distr
ibutions of theta(a) and R(n). We also investigate the asymptotic beha
viour of theta(n), n going to infinity.