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Mutually catalytic branching in the plane: Finite measure states

Abstract:

We study a pair of populations in R2 which undergo diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the local density of the other type. For a diffusion rate sufficiently large compared with the branching rate, the model is constructed as the unique pair of finite measure-valued processes which satisfy a martingale problem involving the collision local time of the solutions. The processes are shown to have densities at fixed times w...

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Publication status:
Published

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Publisher copy:
10.1214/aop/1039548370

Authors


Dawson, DA More by this author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Fleischmann, K More by this author
Perkins, EA More by this author
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Journal:
ANNALS OF PROBABILITY
Volume:
30
Issue:
4
Pages:
1681-1762
Publication date:
2002-10-05
DOI:
ISSN:
0091-1798
URN:
uuid:12b31112-cdfa-46ae-a0a9-996058b0dd6b
Source identifiers:
97465
Local pid:
pubs:97465

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