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

Details Statistical aspects of birth--and--growth stochastic processes Statistical aspects of birth--and--growth stochastic processes

2008-03-18

arxiv.org/abs/0803.2679v3

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simpler notations typos

Scientific paper

10.1016/j.fss.2008.12.011

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.

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