P ] 1 8 M ar 2 00 8 1 Statistical aspects of set – valued continuous time stochastic processes
نویسندگان
چکیده
The paper considers a particular family of set–valued continuous time stochastic processes modeling birth–and–growth processes. The proposed setting allows us to infer the nucleation and the growth processes. A decomposition theorem is established to characterize the nucleation and the growth. As a logical consequence, different consistent set–valued estimators are studied for growth process. Moreover, the nucleation process is studied via the Choquet capacity, and a consistent estimator of the hitting function of nucleation is derived.
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