A continuum individual based model of fragmentation: dynamics of correlation functions

Agnieszka Tanaś

Abstract


An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on  Γ the Markov evolution of which is described in terms of their  correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.

Keywords


Configuration space; individual-based model; birth-and-death process; correlation function; scale of Banach spaces; Ovcyannikov method.

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References


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DOI: http://dx.doi.org/10.17951/a.2015.69.2.73-83
Date of publication: 2015-12-30 22:51:59
Date of submission: 2015-12-30 22:40:24


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