Dynamics of spatial logistic model: finite systems. (English) Zbl 1329.82094
Banasiak, Jacek (ed.) et al., Semigroups of operators – theory and applications. Selected papers based on the presentations at the conference, Bȩdlewo, Poland, October 6–10, 2013. Cham: Springer (ISBN 978-3-319-12144-4/hbk; 978-3-319-12145-1/ebook). Springer Proceedings in Mathematics & Statistics 113, 197-211 (2015).
Summary: The spatial logistic model is a system of point entities (particles) in \(\mathbb R^d\) which reproduce themselves at distant points (dispersal) and die, also due to competition. The states of such systems are probability measures on the space of all locally finite particle configurations. In this paper, we obtain the evolution of states of ’finite systems’, that is, in the case where the initial state is supported on the subset of the configuration space consisting of finite configurations. The evolution is obtained as the global solution of the corresponding Fokker-Planck equation in the space of measures supported on the set of finite configurations. We also prove that this evolution preserves the existence of exponential moments and the absolute continuity with respect to the Lebesgue-Poisson measure.
For the entire collection see [Zbl 1303.47001].
For the entire collection see [Zbl 1303.47001].
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
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