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. AlettiPrimo
;C. MaySecondo
;
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.
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