The full moment problem on subsets of probabilities and point configurations
| Autor: | Maria Infusino, Tobias Kuna |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Correlation function
Infinite dimensional moment problem Point process Random measure Semi-algebraic set Space (mathematics) 01 natural sciences FOS: Mathematics Point (geometry) 0101 mathematics Mathematics Discrete mathematics Applied Mathematics 010102 general mathematics Probability (math.PR) 44A60 28C20 60G55 60G57 Functional Analysis (math.FA) Mathematics - Functional Analysis 010101 applied mathematics Moment problem Moment (mathematics) Mathematics - Probability Analysis Factorial moment Vector space |
| ISSN: | 0022-247X |
| DOI: | 10.48550/arxiv.1802.03582 |
| Popis: | 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 $\mathbb{R}^d$. We consider as $K$ the space of sub-probabilities, probabilities and point configurations on $\mathbb{R}^d$. 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. Comment: 24 pages |
| Databáze: | OpenAIRE |
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