A functional equation whose unknown is P ([0, 1]) valued

Keywords

Statistical learning
Code:
16/2009
Title:
A functional equation whose unknown is P ([0, 1]) valued
Date:
Wednesday 20th May 2009
Author(s):
Aletti, Giacomo; May, Caterina; Secchi, Piercesare
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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 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.