Aletti, Giacomo; Bongiorno, Enea G.; Capasso, Vincenzo Integration in a dynamical stochastic geometric framework. (English) Zbl 1264.60010 ESAIM, Probab. Stat. 15, 402-416 (2011). Summary: 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, non-local, i.e., at a fixed time instant, the growth is the same at each point of the space. Cited in 3 Documents MSC: 60D05 Geometric probability and stochastic geometry 53C65 Integral geometry 60H05 Stochastic integrals Keywords:random closed set; stochastic geometry; birth-and-growth process; set-valued process; Aumann integral; Minkowski sum PDFBibTeX XMLCite \textit{G. Aletti} et al., ESAIM, Probab. Stat. 15, 402--416 (2011; Zbl 1264.60010) Full Text: DOI arXiv