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Ray–Knight representation of flows of branching processes with competition by pruning of Lévy trees

Abstract:

We introduce flows of branching processes with competition, which describe the evolution of general continuous state branching populations in which interactions between individuals give rise to a negative density dependence term. This generalizes the logistic branching processes studied by Lambert (Ann Appl Probab 15(2):1506–1535, 2005). Following the approach developed by Dawson and Li (Ann Probab 40(2):813–857, 2012), we first construct such processes as the solutions of certain flow of sto...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1007/s00440-017-0819-4

Authors


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Institution:
University of Oxford
Division:
MPLS Division
Department:
Statistics
Oxford college:
Magdalen College
Fittipaldi, MC More by this author
Fontbona, J More by this author
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Funding agency for:
Fontbona, J
Publisher:
Springer Verlag Publisher's website
Journal:
Probability Theory and Related Fields Journal website
Volume:
172
Issue:
3-4
Pages:
725–788
Publication date:
2017-12-20
Acceptance date:
2017-11-27
DOI:
EISSN:
1432-2064
ISSN:
0178-8051
Pubs id:
pubs:812239
URN:
uri:deff81c1-fbba-48b4-9520-21f96125ea6f
UUID:
uuid:deff81c1-fbba-48b4-9520-21f96125ea6f
Local pid:
pubs:812239

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