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.

A functional equation whose unknown is P([0,1]) valued / G. Aletti, C. May, P. Secchi. - Milano : Dipartimento di Matematica, Politecnico di Milano, 2009.

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

G. Aletti
Primo
;
C. May
Secondo
;
2009

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.
functional equation in unknown distribution functions ; generalized Polya urn ; reinforced urn process
Settore MAT/06 - Probabilita' e Statistica Matematica
http://arxiv.org/abs/0905.3310
Working Paper
A functional equation whose unknown is P([0,1]) valued / G. Aletti, C. May, P. Secchi. - Milano : Dipartimento di Matematica, Politecnico di Milano, 2009.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/62799
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