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Kondratiev, Yuri; Kozitsky, Yuri

The evolution of states in a spatial population model. (English) Zbl 1404.60124

J. Dyn. Differ. Equations 30, No. 1, 135-173 (2018).
Authors’ abstract: The evolution of states in a spatial population model is studied. The model describes an infinite system of point entities in \(\mathbb R^d\) which reproduce themselves at distant points (disperse) and die with rate that includes a competition term. The system’s states are probability measures on the space of configurations, and their evolution is obtained from a hierarchical chain of differential equations for the corresponding correlation functions derived from the Fokker-Planck equation for the states. Under natural conditions imposed on the model parameters it is proved that the correlation functions evolve in a scale of Banach spaces in such a way that at each moment of time the correlation function corresponds to a unique sub-Poissonian state. Some further properties of the evolution of states constructed in this way are described.
Reviewer: Alexander Iksanov (Kiev)

Cited in 12 Documents

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
92D25 Population dynamics (general)
82C22 Interacting particle systems in time-dependent statistical mechanics

Keywords:

Markov evolution; configuration space; stochastic semigroup; sun-dual semigroup; individual-based model; correlation function; scale of Banach spaces
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