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.
A Functional Equation Whose Unknown is P([0,1]) Valued / G. Aletti, C. May, P. Secchi. - In: JOURNAL OF THEORETICAL PROBABILITY. - ISSN 0894-9840. - 25:4(2012), pp. 1207-1232. [10.1007/s10959-011-0399-7]
A Functional Equation Whose Unknown is P([0,1]) Valued
G. AlettiPrimo
;
2012
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.File | Dimensione | Formato | |
---|---|---|---|
JOTP-639R1.pdf
accesso aperto
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
326.1 kB
Formato
Adobe PDF
|
326.1 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.