The length of the longest head-run in a model with long range dependence

Authors
Lewis, TM
Citation
Tm. Lewis, The length of the longest head-run in a model with long range dependence, J THEOR PR, 14(2), 2001, pp. 357-378
Citations number
26
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THEORETICAL PROBABILITY
ISSN journal
08949840 → ACNP
Volume
14
Issue
2
Year of publication
2001
Pages
357 - 378
Database
ISI
SICI code
0894-9840(200104)14:2<357:TLOTLH>2.0.ZU;2-H
Abstract
In this paper, we construct stationary sequences of random variables {chi ( i): i greater than or equal to 0} taking values +/-1 with probability 1/2 a nd we prove an Erdos Renyi law oi large numbers for the length of the longe st run of consecutive +/- 1's in the sample {chi (0).....chi (n)}. Our mode l, which is called random walk in random scenery. exhibits lung-range. posi tive dependence.