A two-step Markov point process

摘要

The existence and uniqueness are established for atranslation-invariant Gibbs measure corresponding to a spatial pointprocess that has, in addition to inhibition and clustering, thenew-feature of penalizing isolated points. This point process has theso-called two-step Markov property, and the associated density functionis characterized in terms of 2-interaction functions. The asymptoticnormality of certain statistics of the point process is established whenthe size of the observation window tends to IR2