BOUNDS FOR THE EXPECTED NUMBER OF LEVEL-CROSSINGS OF CERTAIN HARMONIZABLE INFINITELY DIVISIBLE PROCESSES

Authors
MARCUS MB SHEN K
Citation
Mb. Marcus et K. Shen, BOUNDS FOR THE EXPECTED NUMBER OF LEVEL-CROSSINGS OF CERTAIN HARMONIZABLE INFINITELY DIVISIBLE PROCESSES, Stochastic processes and their applications, 76(1), 1998, pp. 1-32
Citations number
15
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Stochastic processes and their applications → ACNP
ISSN journal
03044149
Volume
76
Issue
1
Year of publication
1998
Pages
1 - 32
Database
ISI
SICI code
0304-4149(1998)76:1<1:BFTENO>2.0.ZU;2-V
Abstract
Let ENu(0, 1) denote the expected number of crossings of a level u, in a fixed time interval [0,1], by a large class of real valued symmetri c stationary harmonizable infintely divisible processes which includes stationary harmonizable stable processes. Equivalent upper and lower bounds are given for EN0(0, 1) and a precise asymptotic limit is given for ENu(0, 1), as u --> (infinity). (C) 1998 Published by Elsevier Sc ience B.V. All rights reserved.