## Electronic Journal of Probability

### Two Coalescents Derived from the Ranges of Stable Subordinators

#### Abstract

Let $M_\alpha$ be the closure of the range of a stable subordinator of index $\alpha\in ]0,1[$. There are two natural constructions of the $M_{\alpha}$'s simultaneously for all $\alpha\in ]0,1[$, so that $M_{\alpha}\subseteq M_{\beta}$ for $0 \lt \alpha \lt \beta \lt 1$: one based on the intersection of independent regenerative sets and one based on Bochner's subordination. We compare the corresponding two coalescent processes defined by the lengths of complementary intervals of $[0,1]\backslash M_{1-\rho}$ for $0 \lt \rho \lt 1$. In particular, we identify the coalescent based on the subordination scheme with the coalescent recently introduced by Bolthausen and Sznitman.

#### Article information

Source
Electron. J. Probab., Volume 5 (2000), paper no. 7, 17 pp.

Dates
Accepted: 10 November 1999
First available in Project Euclid: 7 March 2016

https://projecteuclid.org/euclid.ejp/1457376442

Digital Object Identifier
doi:10.1214/EJP.v5-63

Mathematical Reviews number (MathSciNet)
MR1768841

Zentralblatt MATH identifier
0949.60034

Subjects
Primary: 60J30
Secondary: 60J25: Continuous-time Markov processes on general state spaces

Rights

#### Citation

Bertoin, Jean; Pitman, Jim. Two Coalescents Derived from the Ranges of Stable Subordinators. Electron. J. Probab. 5 (2000), paper no. 7, 17 pp. doi:10.1214/EJP.v5-63. https://projecteuclid.org/euclid.ejp/1457376442

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