The full moment problem on subsets of probabilities and point configurations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Infusino, Maria¹  Kuna, Tobias² 

[1] Univ Konstanz, Fachbereich Math & Stat, Univ Str 10, D-78457 Constance, Germany

[2] Univ Reading, Dept Math & Stat, POB 220, Reading RG6 6AX, Berks, England

关键词: Infinite dimensional moment problem;    Semi-algebraic set;    Random measure;    Point process;    Correlation function;   

DOI  :  10.1016/j.jmaa.2019.123551

来源: Elsevier

【 摘 要 】

The aim of this paper is to study the full K-moment problem for measures supported on some particular non-linear subsets K of an infinite dimensional vector space. 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 Rd. 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 Infusino et al. (2014) [20]. 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free