Interchangeable Compounds and Thinnings of Random Measures.

摘要

Interchangeable thinnings of point processes and random measures are studied as discrete and continuous compound random measures. Conditions are presented under which these compounds and thinning converge in distribution to random measures that are conditionally infinitely divisible with independent increments, e.g., a Poisson process with a random intensity. Also considered are successive ordered thinnings of point processes and random measures that converge to renewal processes and analogous random measures. As special cases, the author describes high level exceedances of interchangeable processes, and a thinning of a point process where the points are inspected over time according to a renewal process. (Author)