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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Limiting distributions for branching random fields


Author: Joseph Fleischman
Journal: Trans. Amer. Math. Soc. 239 (1978), 353-389
MSC: Primary 60J80
DOI: https://doi.org/10.1090/S0002-9947-1978-0478375-X
MathSciNet review: 0478375
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Abstract: In this paper we derive limiting distributions for branching Brownian motion. The cases considered are where the state space is (1) the line and (2) the plane where (a) initially there's but one particle and (b) where there's initially a random number of independent particles. In all cases, the branching process is critical and we obtain results for the growth of selectively neutral mutant types. We use moment generating functions to derive these results.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0478375-X
Keywords: Branching process, branching diffusion process, random field, mutation
Article copyright: © Copyright 1978 American Mathematical Society