Some Problems of Local Hitting, Scaling, and Conditioning

The aim of this paper is to convey the basic ideas regarding some local hitting and conditioning properties of random measures. Some very general results are obtainable in the special case of simple point processes. Though much of this theory has no counterpart for general random measures, similar results do exist in two cases of special interest—for local time random measures and for Dawson–Watanabe superprocesses. This is an informal account of some of the basic hitting and conditioning properties common to all three cases. Precise statements and proofs will be provided elsewhere.