| Título: | Collision Local Times, Historical Stochastic Calculus, and Competing Species |
| Autores: |
Evans, Steven N.; University of California at Berkeley Perkins, Edwin A.; The University of British Columbia |
| Fecha: | 1998-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics super-process, super-Brownian motion, interaction, local time, historical process, measure-valued Markov branching process, stochastic calculus, martingale measure, random measure 60K35, 60J55, 60H99, 60G57 |
| Descripción: | 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. |
| Idioma: | Inglés |
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3 Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times por Bass, Richard F.; University of Washington,Burdzy, Krzysztof; University of Washington | 8 Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations por Liao, Xiao Xin; University of Strathclyde,Mao, Xuerong; University of Strathclyde |
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