## Annals of Probability

### Trimmed trees and embedded particle systems

#### 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

https://projecteuclid.org/euclid.aop/1089808423

Digital Object Identifier
doi:10.1214/009117904000000090

Mathematical Reviews number (MathSciNet)
MR2073189

Zentralblatt MATH identifier
1048.60063

#### 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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