Integration in a dynamical stochastic geometric framework

Giacomo Aletti, Enea G. Bongiorno, Vincenzo Capasso
2011 E S A I M: Probability & Statistics  
We propose a set-valued framework for the well-posedness of birth-and-growth process. Our birth-and-growth model is rigorously defined as a suitable combination, involving Minkowski sum and Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The simplicity of the used geometrical approach leads us to avoid problems arising by an analytical definition of the front growth such as boundary regularities. In this framework, growth is generally
more » ... isotropic and, according to a mesoscale point of view, it is not local, i.e. for a fixed time instant, growth is the same at each space point.
doi:10.1051/ps/2010009 fatcat:aqksudnuivgvpgnrvsag5b2izy