Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes
type: Item
instance of: scholarly article
title: Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes
zbMATH Open document ID: 0932.60035
DOI: 10.1016/S0304-4149(98)00021-0
author: Michael B. Marcus
author: Kevin H. W. Shen
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: Let \(\{X(t)\), \(t\in [0,1]\}\) be a complex-valued strongly stationary harmonizable \(\xi_g\)-radial process. The authors study stationary harmonizable infinitely divisible processes of the form \(Y(t)=\hbox {Re}\{X(t)\}\). Let \(N_u(0,1)\) be the number of crossings of a level \(u\) by \(Y(t)\) on \([0,1]\). Equivalent upper and lower bounds for \(EN_0(0,1)\) are derived and cruder bounds are presented for \(EN_u(0,1)\) for an arbitrary level \(u\). A limit for \(EN_u(0,1)\) is given as \(u\to \infty \).
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 1364484
zbMATH Keywords: harmonizable infinitely divisible process
zbMATH Keywords: Lévy measure
zbMATH Keywords: Rice's formula
zbMATH Keywords: regularly varying functions
zbMATH Keywords: independent increment
zbMATH Keywords: stable process
reviewed by: Jiří Anděl
MaRDI profile type: Publication
cites work: The expected number of level crossings for stationary, harmonisable, symmetric, stable processes
cites work: Q5544740
cites work: Comparing the tail of an infinitely divisible distribution with integrals of its Levy measure
cites work: Q5512461
cites work: The expected number of zeros of continuous stationary Gaussian processes
cites work: On the convergence of sums of independent Banach space valued random variables
cites work: Q4176721
cites work: Q3997990
cites work: 𝜉-radial processes and random Fourier series
cites work: Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes
cites work: Random Fourier Series with Applications to Harmonic Analysis. (AM-101)
cites work: Mathematical Analysis of Random Noise
cites work: Q3349674
cites work: Necessary and sufficient conditions for sample continuity of random Fourier series and of harmonic infinitely divisible processes
cites work: On a Theorem of Cramer and Leadbetter
Wikidata QID: Q127778756
full work available at URL: s0304-4149(98)00021-0
OpenAlex ID: W1992321372
description: scientific article; zbMATH DE number 1364484