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{1089808423,
author = {Fleischmann, Klaus and Swart, Jan M.},
title = {Trimmed trees and embedded particle systems},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 2179-2221},
language = {en},
url = {http://dml.mathdoc.fr/item/1089808423}
}
Fleischmann, Klaus; Swart, Jan M. Trimmed trees and embedded particle systems. Ann. Probab., Tome 32 (2004) no. 1A, pp. 2179-2221. http://gdmltest.u-ga.fr/item/1089808423/