## Electronic Journal of Probability

### The Joint Law of Ages and Residual Lifetimes for Two Schemes of Regenerative Sets

Amaury Lambert

#### Abstract

We are interested in the component intervals of the complements of a monotone sequence $R_n \subseteq \dots \subseteq R_1$ of regenerative sets, for two natural embeddings. One is based on Bochner's subordination, and one on the intersection of independent regenerative sets. For each scheme, we study the joint law of the so-called ages and residual lifetimes.

#### Article information

Source
Electron. J. Probab., Volume 6 (2001), paper no. 19, 23 pp.

Dates
Accepted: 2 May 2001
First available in Project Euclid: 19 April 2016

https://projecteuclid.org/euclid.ejp/1461097649

Digital Object Identifier
doi:10.1214/EJP.v6-92

Mathematical Reviews number (MathSciNet)
MR1873296

Zentralblatt MATH identifier
0985.60076

Subjects
Primary: 60K05: Renewal theory
Secondary: 60G51: Processes with independent increments; Lévy processes

Rights

#### Citation

Lambert, Amaury. The Joint Law of Ages and Residual Lifetimes for Two Schemes of Regenerative Sets. Electron. J. Probab. 6 (2001), paper no. 19, 23 pp. doi:10.1214/EJP.v6-92. https://projecteuclid.org/euclid.ejp/1461097649

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