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.
"Trimmed trees and embedded particle systems." Ann. Probab. 32 (3) 2179 - 2221, July 2004. https://doi.org/10.1214/009117904000000090