A two-step Markov point process

The existence and uniqueness are established for a translation-invariant Gibbs measure corresponding to a spatial point process that has, in addition to inhibition and clustering, the new-feature of penalizing isolated points. This point process has the so-called two-step Markov property, and the associated density function is characterized in terms of 2-interaction functions. The asymptotic normality of certain statistics of the point process is established when the size of the observation window tends to IR/sup 2/.