Maps Preserving Moment Sequences

Javier Cárcamo ()
Additional contact information
Javier Cárcamo: Universidad Autónoma de Madrid

Journal of Theoretical Probability, 2017, vol. 30, issue 1, 212-232

Abstract: Abstract For any sequence s of real numbers, we consider the class $$\mathcal {L}$$ L of maps (from $$\mathbb {R}^{\mathbb {N}_0}$$ R N 0 to $$\mathbb {R}^{\mathbb {N}_0}$$ R N 0 ) that linearly combine a finite or infinite number of elements of s to obtain the new values of the transformed sequence. We characterize those maps in $$\mathcal {L}$$ L that transform moment sequences into moment sequences in terms of the existence of a stochastic process fulfilling appropriate requirements. Then, well-known stochastic processes are used to construct significant examples of such preserving mappings. As application, we also show that some celebrated numerical sequences (including several important combinatorial sequences) are actually transformed moment sequences.

Keywords: Binomial process; Poisson process; Gamma process; Beta process; Geometric Brownian motion; Stirling numbers; Catalan numbers; Bell numbers; Bell polynomials; Primary: 44A60; 60K99; Secondary: 05A15; 11B73 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-015-0647-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:30:y:2017:i:1:d:10.1007_s10959-015-0647-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-015-0647-3

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().