Survival functions and contact distribution functions for inhomogeneous, stochastic geometric marked point processes

Many real phenomena, including phase changes, such as crystallization processes, tumor growth, forest growth, etc., may be modelled as stochastic birth-and-growth processes, in which crystals develop from points (nuclei) that are born at random both in space and time. In this paper, we revisit these processes by classical methods of survival analysis with specific reference to the role played by the survival function and the corresponding hazard rate with respect to capture of a point by the so called crystalline phase. General expressions for the hazard and survival functions associated with a point are provided. Known results for Poisson type processes follow as particular cases. Further, a link between hazard functions and contact distribution function of stochastic geometry is also obtained. Copyright