The full moment problem on subsets of probabilities and point configurations

Infusino, M. and Kuna, T. (2020) The full moment problem on subsets of probabilities and point configurations. Journal of Mathematical Analysis and Applications, 483 (1). 123551. ISSN 0022-247X doi: 10.1016/j.jmaa.2019.123551

Abstract/Summary

The aim of this paper is to study the full K−moment problem for measures supported on some particular infinite dimensional non-linear spaces K. We focus on the case of random measures, that is K is a subset of all non-negative Radon measures on R d . We consider as K the space of sub-probabilities, probabilities and point configurations on R d . For each of these spaces we provide at least one representation as a generalized basic closed semi-algebraic set to apply the main result in [J. Funct. Anal., 267 (2014) no.5: 1382–1418]. We demonstrate that this main result can be significantly improved by further considerations based on the particular chosen representation of K. In the case when K is a space of point configurations, the correlation functions (also known as factorial moment functions) are easier to handle than the ordinary moment functions. Hence, we additionally express the main results in terms of correlation functions.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/86544
Identification Number/DOI	10.1016/j.jmaa.2019.123551
Refereed	Yes
Divisions	Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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