Open Access
June 1996 Asymptotic fluctuations and critical dimension for a two-level branching system
Luis G. Gorostiza
Bernoulli 2(2): 109-132 (June 1996). DOI: 10.3150/bj/1193839219


The high-density asymptotic behaviour of a two-level branching system in Rd is studied. In the finite-variance case, a fluctuation limit process is obtained which is characterized as a generalized Ornstein-Uhlenbeck process. In the case of critical branching at the two levels the long-time behaviour of the fluctuation limit process is shown to have critical dimension , where α is the index of the symmetric stable process representing the underlying particle motion. The same critical dimension has been obtained recently for the related (but qualitatively different) two-level superprocess. The fluctuation analysis uses different and simpler tools than the superprocess analysis.


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Luis G. Gorostiza. "Asymptotic fluctuations and critical dimension for a two-level branching system." Bernoulli 2 (2) 109 - 132, June 1996.


Published: June 1996
First available in Project Euclid: 31 October 2007

zbMATH: 0870.60087
MathSciNet: MR1410133
Digital Object Identifier: 10.3150/bj/1193839219

Keywords: asymptotic fluctuations , critical dimension , two-level branching system

Rights: Copyright © 1996 Bernoulli Society for Mathematical Statistics and Probability

Vol.2 • No. 2 • June 1996
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