Conditional expectation for finitely additive probabilities.

Luis A. Sarabia

Trabajos de Estadística e Investigación Operativa (1982)

  • Volume: 33, Issue: 1, page 64-85
  • ISSN: 0041-0241

Abstract

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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).

How to cite

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Sarabia, Luis A.. "Esperanza condicionada para probabilidades finitamente aditivas.." Trabajos de Estadística e Investigación Operativa 33.1 (1982): 64-85. <http://eudml.org/doc/40677>.

@article{Sarabia1982,
author = {Sarabia, Luis A.},
journal = {Trabajos de Estadística e Investigación Operativa},
keywords = {Probabilidad; Esperanza condicionada; finitely additive probability; conditional expectation; Dunford-Schwartz integral},
language = {spa},
number = {1},
pages = {64-85},
title = {Esperanza condicionada para probabilidades finitamente aditivas.},
url = {http://eudml.org/doc/40677},
volume = {33},
year = {1982},
}

TY - JOUR
AU - Sarabia, Luis A.
TI - Esperanza condicionada para probabilidades finitamente aditivas.
JO - Trabajos de Estadística e Investigación Operativa
PY - 1982
VL - 33
IS - 1
SP - 64
EP - 85
LA - spa
KW - Probabilidad; Esperanza condicionada; finitely additive probability; conditional expectation; Dunford-Schwartz integral
UR - http://eudml.org/doc/40677
ER -

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