Asymptotic behaviour of measurevalued critical branching processes
Author:
Alison M. Etheridge
Journal:
Proc. Amer. Math. Soc. 118 (1993), 12511261
MSC:
Primary 60J80; Secondary 60G57, 60J60
MathSciNet review:
1100650
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Abstract: Measurevalued branching processes can be characterized in terms of the Laplace transform of their transition densities and this gives rise to a second order nonlinear p.d.e.the evolution equation of the process. We write the solution to this evolution equation as a series, each of whose coefficients is expressed in terms of the linear semigroup corresponding to the spatial part of the measurevalued process. From this we obtain a simple proof that if the spatial part of the process is a recurrent (resp., transient) Markov process on a standard Borel space and the initial value of the process is an invariant measure of this spatial process, then the process has no (resp., has a unique) nontrivial limiting distribution.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919931100650X
PII:
S 00029939(1993)1100650X
Keywords:
Measurevalued diffusions,
critical branching process,
diffusion approximation,
asymptotic distribution
Article copyright:
© Copyright 1993
American Mathematical Society
