Integration in a dynamical stochastic geometric framework

Giacomo Aletti, Enea G. Bongiorno, Vincenzo Capasso

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer review

Abstract

Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary regularities arising from an analytical definition of the front growth. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, is non local, i.e. at a fixed time instant, growth is the same at each point of the space.

Lingua originaleInglese
pagine (da-a)233-248
Numero di pagine16
RivistaESAIM - Probability and Statistics
Volume15
DOI
Stato di pubblicazionePubblicato - mag 2011
Pubblicato esternamente

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