## Necessary and sufficient conditions for realizability of point processesTools
Kuna, T., Lebowitz, J. and Speer, E.
(2011)
Full text not archived in this repository. To link to this article DOI: 10.1214/10-AAP703 ## Abstract/SummaryWe give necessary and sufficient conditions for a pair of (generali- zed) functions 1(r1) and 2(r1, r2), ri 2X, to be the density and pair correlations of some point process in a topological space X, for ex- ample, Rd, Zd or a subset of these. This is an infinite-dimensional version of the classical “truncated moment” problem. Standard tech- niques apply in the case in which there can be only a bounded num- ber 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 re- quirement—the existence of a finite third order moment. We general- ize the latter conditions in two distinct ways when X is not compact.
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