HOW MANY RANDOM-WALKS CORRESPOND TO A GIVEN SET OF RETURN PROBABILITIES TO THE ORIGIN

Authors
DETTE H STUDDEN WJ
Citation
H. Dette et Wj. Studden, HOW MANY RANDOM-WALKS CORRESPOND TO A GIVEN SET OF RETURN PROBABILITIES TO THE ORIGIN, Stochastic processes and their applications, 64(1), 1996, pp. 17-30
Citations number
9
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Stochastic processes and their applications → ACNP
ISSN journal
03044149
Volume
64
Issue
1
Year of publication
1996
Pages
17 - 30
Database
ISI
SICI code
0304-4149(1996)64:1<17:HMRCTA>2.0.ZU;2-X
Abstract
We consider the class of simple random walks or birth and death chains on the nonnegative integers. The set of return probabilities P-00(n), n greater than or equal to 0, uniquely determines the spectral measur e of the process. We characterize the class of simple random walks wit h the same spectral measure or same return probabilities to the origin . The analysis is based on the spectral theory developed by Karlin and McGregor (1959), continued fractions and canonical moments.