Abstract
Most mathematical models introduced in the life and social sciences literature that describe inherently spatial phenomena of interacting populations consist of systems of ordinary differential equations or stochastic counterparts assuming global interactions such as the logistic growth process and the Moran model. These models, however, leave out any spatial structure, while past research has identified the spatial component as an important factor in how communities are shaped, and spatial models can result in predictions that differ from nonspatial models.
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References
P. Clifford and A. Sudbury. A model for spatial conflict. Biometrika, 60:581–588, 1973.
R. L. Dobrušin. Markov processes with a large number of locally interacting components: Existence of a limit process and its ergodicity. Problemy Peredači Informacii, 7(2):70–87, 1971.
R. L. Dobrušin. Markov processes with a large number of locally interacting components: The invertible case and certain generalizations. Problemy Peredači Informacii, 7(3):57–66, 1971.
R. Durrett. Ten lectures on particle systems. In Lectures on probability theory (Saint-Flour, 1993), volume 1608 of Lecture Notes in Math., pages 97–201. Springer-Verlag, Berlin, 1995.
T. E. Harris. Nearest-neighbor Markov interaction processes on multidimensional lattices. Adv. Math., 9:66–89, 1972.
T. E. Harris. Contact interactions on a lattice. Ann. Prob., 2:969–988, 1974.
R. A. Holley and T. M. Liggett. Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Prob., 3(4):643–663, 1975.
T. M. Liggett. Interacting particle systems, volume 276 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, New York, 1985.
T. M. Liggett. Stochastic interacting systems: contact, voter, and exclusion processes, volume 324 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1999.
Frank Spitzer. Interaction of Markov processes. Adv. Math., 5:246–290 (1970), 1970.
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Lanchier, N. (2017). Interacting particle systems. In: Stochastic Modeling. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-50038-6_14
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DOI: https://doi.org/10.1007/978-3-319-50038-6_14
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