IJPAM: Volume 55, No. 2 (2009)
ON THE USE OF THE LAPLACE FUNCTIONAL
FOR TWO-LEVEL BRANCHING SYSTEMS
FOR TWO-LEVEL BRANCHING SYSTEMS
Kenneth J. Hochberg
, Andreas Greven
Department of Mathematics
Bar-Ilan University
Ramat-Gan, 52900, ISRAEL
e-mail: hochberg@macs.biu.ac.il
Mathematisches Institut
Universität Erlangen-Nürnberg
Bismarckstraße 1 1/2, Erlangen, D-91054, GERMANY
e-mail: greven@mi.uni-erlangen.de
, Andreas Greven
Department of Mathematics
Bar-Ilan University
Ramat-Gan, 52900, ISRAEL
e-mail: hochberg@macs.biu.ac.il
Mathematisches Institut
Universität Erlangen-Nürnberg
Bismarckstraße 1 1/2, Erlangen, D-91054, GERMANY
e-mail: greven@mi.uni-erlangen.de
Abstract.The two-level superprocess arises as
the high-density diffusion limit of a two-level
branching Brownian motion, in which particles are grouped into superparticles in which
they collectively replicate or vanish according to some branching mechanism, in addition
to the motion and branching of the individual particles themselves. Here, the use of the
Laplace functional in the analysis of such two-level superprocesses is described.
Received: February 11, 2008
AMS Subject Classification: 60K35, 60G57
Key Words and Phrases: branching process, superprocess, multilevel branching
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2