WIAS Preprint No. 793, (2002)

Trimmed trees and embedded particle systems


  • Fleischmann, Klaus
  • Swart, Jan

2010 Mathematics Subject Classification

  • 60J80 60G57 60J60 60K35


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


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, 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.

Appeared in

  • Ann. Probab., 32 (2004), pp. 2179--222

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