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 Electronic Journal of Probability > Vol. 3 (1998) > Paper 5 open journal systems 


Collision Local Times, Historical Stochastic Calculus, and Competing Species

Steven N. Evans, University of California at Berkeley
Edwin A. Perkins, The University of British Columbia


Abstract
Branching measure-valued diffusion models are investigated that can be regarded as pairs of historical Brownian motions modified by a competitive interaction mechanism under which individuals from each population have their longevity or fertility adversely affected by collisions with individuals from the other population. For 3 or fewer spatial dimensions, such processes are constructed using a new fixed-point technique as the unique solution of a strong equation driven by another pair of more explicitly constructible measure-valued diffusions. This existence and uniqueness is used to establish well-posedness of the related martingale problem and hence the strong Markov property for solutions. Previous work of the authors has shown that in 4 or more dimensions models with the analogous definition do not exist.


Full text: PDF

Pages: 1-120

Published on: April 8, 1998
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Electronic Journal of Probability. ISSN: 1083-6489