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

TL;DR

This paper investigates set-valued stochastic processes modeling birth-and-growth phenomena, providing decomposition theorems, estimators for growth and nucleation, and insights into their statistical properties.

Contribution

It introduces a novel framework for analyzing birth-and-growth processes with decomposition theorems and consistent estimators for nucleation and growth.

Findings

Decomposition theorem characterizes nucleation and growth.

Consistent estimators for growth process are developed.

A new estimator for the nucleation hitting function is proposed.

Abstract

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.