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Return times in a process generated by a typical partition

SYSNO ASEP	0330009
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Return times in a process generated by a typical partition
Title	Doby návratu v procesu generovaném typickým rozkladem
Author(s)	Grzegorek, P. (PL) Kupsa, Michal (UTIA-B)_{RID, ORCID}
Source Title	Nonlinearity. - : Institute of Physics Publishing - ISSN 0951-7715 Roč. 22, č. 2 (2009), s. 371-379
Number of pages	9 s.
Language	eng - English
Country	GB - United Kingdom
Keywords	return times ; exponential distribution ; mixing process ; hitting times ; adding machine
Subject RIV	BA - General Mathematics
R&D Projects	KJB100750901 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z10750506 - UTIA-B (2005-2011)
UT WOS	000262584500007
DOI	10.1088/0951-7715/22/2/007
Annotation	In Downarowicz and Lacroix (2006 Law of series) and Downarowicz et al (2007 ESAIM P&S), the authors show that for every ergodic aperiodic dynamical system, the process generated by a typical partition has the following property: the zero function is a pointwise limit, along a subsequence of lengths nk of upper density 1 and with probabilities increasing to 1, of the distribution functions of the normalized (i.e. appropriately scaled) hitting times to cylinder sets of lengths nk. Of course, this is the smallest possible limit distribution. We indicate two classes of systems where at least one more limit distribution coexists, and occurs with the same 'strength' (i.e. for every typical process, along a subsequence of lengths of upper density 1 and with probabilities increasing to 1): in α-mixing systems this is the exponential limit distribution.
Workplace	Institute of Information Theory and Automation
Contact	Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
Year of Publishing	2010

Number of the records: 1