Necessary and sufficient conditions for realizability of point processes

Details Necessary and sufficient conditions for realizability of point processes Necessary and sufficient conditions for realizability of point processes

2009-10-09

arxiv.org/abs/0910.1710v2

Annals of Applied Probability 2011, Vol. 21, No. 4, 1253-1281

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP703 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP703

We give necessary and sufficient conditions for a pair of (generalized) functions $\rho_1(\mathbf{r}_1)$ and $\rho_2(\mathbf{r}_1,\mathbf{r}_2)$, $\mathbf{r}_i\in X$, to be the density and pair correlations of some point process in a topological space $X$, for example, $\mathbb {R}^d$, $\mathbb {Z}^d$ or a subset of these. This is an infinite-dimensional version of the classical "truncated moment" problem. Standard techniques apply in the case in which there can be only a bounded number of points in any compact subset of $X$. Without this restriction we obtain, for compact $X$, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further requirement---the existence of a finite third order moment. We generalize the latter conditions in two distinct ways when $X$ is not compact.

Affiliated with

Also associated with

No associations

Rating

Necessary and sufficient conditions for realizability of point processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Necessary and sufficient conditions for realizability of point processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Necessary and sufficient conditions for realizability of point processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-51248