A Functional Equation Whose Unknown is $\mathcal{P}([0,1])$ Valued

Giacomo Aletti (), Caterina May () and Piercesare Secchi ()
Additional contact information
Giacomo Aletti: Università degli Studi di Milano
Caterina May: Università del Piemonte Orientale
Piercesare Secchi: Politecnico di Milano

Journal of Theoretical Probability, 2012, vol. 25, issue 4, 1207-1232

Abstract: Abstract We study a functional equation whose unknown maps a Euclidean space into the space of probability distributions on [0,1]. We prove existence and uniqueness of its solution under suitable regularity and boundary conditions, we show that it depends continuously on the boundary datum, and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means of a Randomly Reinforced Urn with different reinforcement distributions having equal means. The general solution to the functional equation defines a new parametric collection of distributions on [0,1] generalizing the Beta family.

Keywords: Functional equation in unknown distribution functions; Generalized Pólya urn; Reinforced urn process; 62E10; 39B52; 62E20 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-011-0399-7 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:25:y:2012:i:4:d:10.1007_s10959-011-0399-7

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

DOI: 10.1007/s10959-011-0399-7

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 ().