Statistical aspects of fuzzy monotone set-valued stochastic processes. Application to birth-and-growth processes

Authors:
Giacomo Aletti;Enea G. Bongiorno;Vincenzo Capasso
Affiliations:
Department of Mathematics, University of Milan, via Saldini 50, 10133 Milan, Italy;Department of Mathematics, University of Milan, via Saldini 50, 10133 Milan, Italy;Department of Mathematics, University of Milan, via Saldini 50, 10133 Milan, Italy
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

The paper considers a particular family of fuzzy monotone set-valued stochastic processes. The proposed setting allows us to investigate suitable @a-level sets of such processes, modeling birth-and-growth processes. 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.