Post date: 26-Apr-2014 17:18:43
Giovedì 10 Aprile 2014, ore 11.30, Sala Riunioni primo piano
Relatore: Dott. Bongiorno Enea
Titolo: Integration in a dynamical stochastic geometric framework. Statistical Aspects.
Abstract: Motivated by the well-posedness of birth-and-growth processes under suitable assumptions, a stochastic geometrical differential equation and, hence, a stochastic geometrical dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving Minkowski sum and Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometrical approach permits to avoid 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 not local, i.e. for a fixed time instant, growth is the same at each point of the space. A decomposition theorem is established to characterize the nucleation and the growth. As a consequence, different consistent set-valued estimators are studied for growth process. Moreover, the nucleation process is studied via the hitting function, and a consistent estimator of the nucleation hitting function is derived.
References:
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(doi: 10.1016/j.spl.2012.01.011) RevV: http://hdl.handle.net/2434/169672
G.Aletti, E.G.B., V.Capasso. Integration in a dynamical stochastic geometric framework. ESAIM: Probability and Statistics, 15 (2011) 402--416.
The original publication is available at www.edpsciences.org/ps (doi: 10.1051/ps/2010009) PubV:http://hdl.handle.net/2434/170453
G.Aletti, E.G.B., V.Capasso. Statistical aspects of fuzzy monotone set-valued stochastic processes. Application to birth-and-growth processes. Fuzzy Sets and Systems 160 (2009), pp. 3140-3151.
(doi: 10.1016/j.fss.2008.12.011) RevV: http://hdl.handle.net/2434/67515