Título inglés | Conditional expectation for finitely additive probabilities. |
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Título español | Esperanza condicionada para probabilidades finitamente aditivas. |
Autor/es | Sarabia, Luis A. |
Organización | Col. Univ. Burgos Univ. Valladolid, Burgos, España |
Revista | 0041-0241 |
Publicación | 1982, 33 (1): 64-85, 15 Ref. |
Tipo de documento | articulo |
Idioma | Español |
Resumen inglés | Let (Ω, θ, J) be a finitely additive probabilistic space formed by any set Ω, an algebra of subsets θ and a finitely additive probability J. In these conditions, if F belongs to V1(Ω, θ, J) there exists f, element of the completion of L1(Ω, θ, J), such that F(E) = ∫E f dJ for all E of θ and conversely. The integral representation gives sense to the following result, which is the objective of this paper, in terms of the point function: if β is a subalgebra of θ, for every F of V1(Ω, θ, J) there exists a unique element of V1(Ω, θ, J) which we note down by E(F/β), conditional expectation of F given β. E(F/β) is characterized by (E(F/β), G) = (F, G) for every G of V∞(Ω, β, J). Aside from this, the mapping E(./β): V1(Ω, θ, J) → V1(Ω, β, J) is lineal, positive, contractive, idempotent and E(J/β) = J. If F is of Vp(Ω, θ, J), p > 1, E(F/β) is of Vp(Ω, β, J). |
Clasificación UNESCO | 120804 |
Palabras clave español | Probabilidad ; Esperanza condicionada |
Código MathReviews | MR0697208 |
Código Z-Math | Zbl 0513.60006 |
Acceso al artículo completo |