Construction of a specification from its singleton part

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We state a construction theorem for specifications starting from single-site conditional probabilities (singleton part). We consider general single-site spaces and kernels that are absolutely continuous with respect to a chosen product measure (free measure). Under a natural order-consistency assumption and weak non-nullness requirements we show existence and uniqueness of the specification extending the given singleton part. We determine conditions granting the continuity of the specification. In addition, we show that, within a class of measures with suitable support properties, consistency with singletons implies consistency with the full specification.
19 pages. Version to appear in ALEA. We added Proposition 4.3 and made small corrections with respect to version 1

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Probability, 82B05

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http://salesiana.dossiersoluciones.com/handle/123456789/100884

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409539
 http://arxiv.org/abs/math/0409539

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arXiv