An explicit estimate of sojourning time by intermittency with elementary method
type: Item
instance of: scholarly article
title: An explicit estimate of sojourning time by intermittency with elementary method
zbMATH Open document ID: 0543.58020
author: Jun Kigami
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: The paper studies the 1-parameter ''bifurcation'' family \(F(\mu,x)=\mu +x- x^ 2+\mu xf(\mu,x)+x^ 3g(x),\) where f and g are continuous at \(x=0\), and its random perturbations of the form \((X_{n+1}=F(\mu,X_ n)+| \mu |^{1+\theta}\zeta_ n\) where \(\theta>0\) and \(\zeta_ n\) is a bounded random variable. The author proves that for suitable \(\delta>0\) one gets the following asymptotic behavior of sojourning time in [- \(\delta\),\(\delta]\), \(\lim_{\mu \uparrow 0}\sqrt{-\mu}\min \{n:\quad X_ n<-\delta \}\).
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 58E07
zbMATH DE Number: 3864155
zbMATH Keywords: laminar phase
zbMATH Keywords: bifurcation
zbMATH Keywords: random variable
zbMATH Keywords: sojourning time
reviewed by: Yuri Kifer
MaRDI profile type: Publication
full work available at URL: pjaa.59.459
OpenAlex ID: W2090597454
cites work: Q3701080
cites work: On the bifurcation of maps of the interval
cites work: Intermittency in the presence of noise
DOI: 10.3792/PJAA.59.459
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description: scientific article; zbMATH DE number 3864155