The Annals of Probability

Trimmed trees and embedded particle systems

Klaus Fleischmann and Jan M. Swart

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Abstract

In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller underlying motion on compact spaces, we identify the trimmed tree, which turns out to be a binary splitting particle system with a new underlying motion that is a compensated h-transform of the old one. We show how trimmed trees may be estimated from above by embedded binary branching particle systems.

Article information

Source
Ann. Probab., Volume 32, Number 3 (2004), 2179-2221.

Dates
First available in Project Euclid: 14 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1089808423

Digital Object Identifier
doi:10.1214/009117904000000090

Mathematical Reviews number (MathSciNet)
MR2073189

Zentralblatt MATH identifier
1048.60063

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G57: Random measures 60J60: Diffusion processes [See also 58J65] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
(Historical) superprocess binary branching Poissonization embedded particle system trimmed tree compensated h-transform finite ancestry property

Citation

Fleischmann, Klaus; Swart, Jan M. Trimmed trees and embedded particle systems. Ann. Probab. 32 (2004), no. 3, 2179--2221. doi:10.1214/009117904000000090. https://projecteuclid.org/euclid.aop/1089808423


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