The Evolution of States in a Spatial Population Model

Kondratiev Y, Kozitsky Y (2018)
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 30(1): 135-173.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Kozitsky, Yuri
Abstract / Bemerkung
The evolution of states in a spatial population model is studied. The model describes an infinite system of point entities in 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.
Stichworte
Markov evolution; Configuration space; Stochastic semigroup; Sun-dual; semigroup; Individual-based model; Correlation function; Scale of Banach; spaces
Erscheinungsjahr
2018
Zeitschriftentitel
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
Band
30
Ausgabe
1
Seite(n)
135-173
ISSN
1040-7294
eISSN
1572-9222
Page URI
https://pub.uni-bielefeld.de/record/2919068

Zitieren

Kondratiev Y, Kozitsky Y. The Evolution of States in a Spatial Population Model. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. 2018;30(1):135-173.
Kondratiev, Y., & Kozitsky, Y. (2018). The Evolution of States in a Spatial Population Model. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 30(1), 135-173. doi:10.1007/s10884-016-9526-6
Kondratiev, Y., and Kozitsky, Y. (2018). The Evolution of States in a Spatial Population Model. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 30, 135-173.
Kondratiev, Y., & Kozitsky, Y., 2018. The Evolution of States in a Spatial Population Model. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 30(1), p 135-173.
Y. Kondratiev and Y. Kozitsky, “The Evolution of States in a Spatial Population Model”, JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, vol. 30, 2018, pp. 135-173.
Kondratiev, Y., Kozitsky, Y.: The Evolution of States in a Spatial Population Model. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. 30, 135-173 (2018).
Kondratiev, Yuri, and Kozitsky, Yuri. “The Evolution of States in a Spatial Population Model”. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 30.1 (2018): 135-173.
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2020-10-29T20:00:00Z

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