(1) Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
Abstract:
It is well-known that the distribution of a point process defined on a carrier space is uniquely characterised by its finite dimensional joint distributions of counts on disjoint subsets of . In this note, we investigate the common structure of point processes whose distributions are specified by their one dimensional distributions. We also show that, if is such a point process, then a sequence of point processes {n} converges in distribution to if and only if {n(B)} converges in distribution to (B) for a suitably rich class of sets B.
Supported by ARC Discovery project number DP0209179
Mathmatics Subject Classification (2000):Primary 60G55; Secondary 60E05, 60B10
AcknowledgementI would like to thank a referee for his valuable suggestions on the presentation of this paper.