Abstract
We give a complete characterization of the domain of attraction of fixed points of branching Brownian motion (BBM) with critical drift. Prior to this classification, we introduce a suitable metric space of locally finite point measures on which we prove 1) that the BBM with critical drift is a well-defined Markov process and 2) that it satisfies the Feller property. Several applications of this characterization are given.
Funding Statement
The first author was supported by Nation Key R&D Program of China 2022YFA1006500. The second author was supported by the Institut Universitaire de France (IUF) and the French ANR grant ANR-21-CE40-0003. The third author was supported by project PIC RTI4001: Mathematics, Theoretical Sciences and Science Education.
Acknowledgments
The second author wishes to thank the ICJ probability lunch team for an enlightening discussion which led to the viewpoint in Proposition 6.3. In addition, the second author is also affiliated to Institut Universitaire de France (IUF).
Citation
Xinxin Chen. Christophe Garban. Atul Shekhar. "Domain of attraction of the fixed points of Branching Brownian motion." Ann. Appl. Probab. 34 (6) 5351 - 5387, December 2024. https://doi.org/10.1214/24-AAP2093
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