Global regime for general additive functionals of conditioned Bienaymé-Galton-Watson trees

We give an invariance principle for very general additive functionals of conditioned Bienaymé-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Lévy tree. This include...

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Bibliographic Details
Published in:Probability theory and related fields 2022-02, Vol.182 (1-2), p.277-351
Main Authors: Abraham, Romain, Delmas, Jean-François, Nassif, Michel
Format: Article
Language:English
Subjects:
Economics
Finance
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Phase transitions
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Theoretical
Trees
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Summary:We give an invariance principle for very general additive functionals of conditioned Bienaymé-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Lévy tree. This includes the case when the offspring distribution has finite variance (the Lévy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending on the size and height.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-021-01095-9