The Annals of Probability

Regenerative Systems on the Real Line

H. Kaspi and B. Maisonneuve

Full-text: Open access

Abstract

We consider regenerative systems on the real line and study their structure. Local times and exit systems are defined. This leads to time changes and last exit decompositions. We establish a correspondence between stationary regenerative systems and Markov additive processes which are stationary in the space component.

Article information

Source
Ann. Probab., Volume 16, Number 3 (1988), 1306-1332.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991693

Digital Object Identifier
doi:10.1214/aop/1176991693

Mathematical Reviews number (MathSciNet)
MR942771

Zentralblatt MATH identifier
0655.60064

JSTOR
links.jstor.org

Subjects
Primary: 60K05: Renewal theory
Secondary: 60J55: Local time and additive functionals 60J25: Continuous-time Markov processes on general state spaces 60J50: Boundary theory 60G17: Sample path properties

Keywords
Regenerative systems local times exit systems time changes last exit decompositions Markov additive processes stationarity

Citation

Kaspi, H.; Maisonneuve, B. Regenerative Systems on the Real Line. Ann. Probab. 16 (1988), no. 3, 1306--1332. doi:10.1214/aop/1176991693. https://projecteuclid.org/euclid.aop/1176991693


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