Trimmed trees and embedded particle systems

Details Trimmed trees and embedded particle systems Trimmed trees and embedded particle systems

2004-10-05

arxiv.org/abs/math/0410113v1

Annals of Probability 2004, Vol. 32, No. 3A, 2179-2221

Mathematics

Probability

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imsta

Scientific paper

10.1214/009117904000000090

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.

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