A Functional Equation Whose Unknown is P([0,1]) Valued

Giacomo Aletti, Caterina May, Piercesare Secchi

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer review

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.

Lingua originaleInglese
pagine (da-a)1207-1232
Numero di pagine26
RivistaJournal of Theoretical Probability
Volume25
Numero di pubblicazione4
DOI
Stato di pubblicazionePubblicato - nov 2012

Fingerprint

Entra nei temi di ricerca di 'A Functional Equation Whose Unknown is P([0,1]) Valued'. Insieme formano una fingerprint unica.

Cita questo