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.

Integration in a dynamical stochastic geometric framework / G. Aletti, E.G. Bongiorno, V. Capasso. - In: ESAIM: PROBABILITY AND STATISTICS. - ISSN 1262-3318. - 15(2011 Jan), pp. 402-416.

Integration in a dynamical stochastic geometric framework

G. Aletti
Primo
;
E.G. Bongiorno
Secondo
;
V. Capasso
Ultimo
2011

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.
Random closed set ; Stochastic geometry ; Birth–and–growth process ; Set–valued process ; Aumann integral ; Minkowski sum
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore SECS-S/01 - Statistica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/170453
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