标题： 出生-成长随机过程的统计方面 显示英文标题

标题： Statistical aspects of birth--and--growth stochastic processes

摘要： 本文研究了一类建模出生-增长过程的集值随机过程族。 所提出的设定允许我们探讨成核和生长过程。 建立了一个分解定理以刻画成核和生长。 由此，研究了不同一致的集值生长过程估计量。 此外，通过击中函数研究了成核过程，并推导出成核击中函数的一致估计量。 显示英文摘要

摘要： The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the 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.