The paper considers a particular family of fuzzy monotone set-valued stochastic processes. The proposed setting allows us to investigate suitable α-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.
Statistical aspects of fuzzy monotone set-valued stochastic processes. Application to birth-and-growth processes / G. Aletti, E. Bongiorno, V. Capasso. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - 160:21(2009), pp. 3140-3151. [10.1016/j.fss.2008.12.011]
Statistical aspects of fuzzy monotone set-valued stochastic processes. Application to birth-and-growth processes
G. AlettiPrimo
;E. BongiornoSecondo
;V. CapassoUltimo
2009
Abstract
The paper considers a particular family of fuzzy monotone set-valued stochastic processes. The proposed setting allows us to investigate suitable α-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.File | Dimensione | Formato | |
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