Hitting and returning to rare events for all alpha-mixing processes

Miguel Abadi and Benoit Saussol

Stochastic Processes and their Applications, 2011, vol. 121, issue 2, 314-323

Abstract: We prove that for any [alpha]-mixing stationary process the hitting time of any n-string An converges, when suitably normalized, to an exponential law. We identify the normalization constant [lambda](An). A similar statement holds also for the return time. To establish this result we prove two other results of independent interest. First, we show a relation between the rescaled hitting time and the rescaled return time, generalizing a theorem of Haydn, Lacroix and Vaienti. Second, we show that for positive entropy systems, the probability of observing any n-string in n consecutive observations goes to zero as n goes to infinity.

Keywords: Mixing; processes; Hitting; times; Repetition; times; Return; times; Rare; event; Exponential; approximation (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00259-0
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:121:y:2011:i:2:p:314-323

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().