Stationary Markov processes related to stable Ornstein-Uhlenbeck processes and the additive coalescent

Steven N. Evans and Jim Pitman

Stochastic Processes and their Applications, 1998, vol. 77, issue 2, 175-185

Abstract: We consider some classes of stationary, counting-measure-valued Markov processes and their companions under time reversal. Examples arise in the Lévy-Itô decomposition of stable Ornstein-Uhlenbeck processes, the large-time asymptotics of the standard additive coalescent, and extreme value theory. These processes share the common feature that points in the support of the evolving counting measure are born or die randomly, but each point follows a deterministic flow during its lifetime.

Keywords: Coalescent; Flow; Jumping; Markov; process; Ornstein-Uhlenbeck; Piecewise; deterministic; Point; process; Poisson; Measure-valued; Stable; Stationary; Extreme; value (search for similar items in EconPapers)
Date: 1998
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(98)00042-8
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:77:y:1998:i:2:p:175-185

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 ().