On time- and cycle-stationarity

Hermann Thorisson

Stochastic Processes and their Applications, 1995, vol. 55, issue 2, 183-209

Abstract: Consider processes split into cycles by a sequence of random times (called points). The standard Palm relationship between stationary processes with cycles and processes with stationary cycles is produced in two transparent steps: length-biasing and re-centring. It has the following standard intuitive interpretation: the process with stationary cycles behaves like the stationary one conditioned on a point at time zero. A less known modification of this relationship is produced by conditioning on the invariant [sigma]-algebra before length-biasing. It has the following intuitive interpretation: the stationary process behaves like the cycle-stationary one centred at a time chosen at random on the line. The present approach leads to strong conditioning, limit and coupling results motivating these interpretations.

Keywords: Palm; theory; Stationarity; Shift-coupling (search for similar items in EconPapers)
Date: 1995
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(94)00038-U
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:55:y:1995:i:2:p:183-209

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 ().