Necessary and sufficient conditions for realizability of point processes
| Autor: | Kuna, Tobias, Lebowitz, Joel L., Speer, Eugene R. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Annals of Applied Probability 2011, Vol. 21, No. 4, 1253-1281 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/10-AAP703 |
| Popis: | 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. Comment: Published in at http://dx.doi.org/10.1214/10-AAP703 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | arXiv |
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