Invariance Properties of the Conditional Independence Relation
van Putten, C. ; van Schuppen, J. H.
Ann. Probab., Tome 13 (1985) no. 4, p. 934-945 / Harvested from Project Euclid
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The conditional independence relation for a triple of $\sigma$-algebras is investigated. For certain operations on this relation, necessary and sufficient conditions are derived such that these operations leave the relation invariant. Examples of such operations are the enlargement or reduction of the $\sigma$-algebras, and an absolute continuous change of measure. A projection operator for $\sigma$-algebras is defined and some of its properties are stated. The $\sigma$-algebraic realization problem is briefly discussed.
Publié le : 1985-08-14
Classification:  Conditional independence relation,  invariance properties,  projection operator,  $\sigma$-algebraic realization problem,  stochastic realization problem,  60A10,  60G05,  62B05,  62B20,  93E03 
@article{1176992915,
     author = {van Putten, C. and van Schuppen, J. H.},
     title = {Invariance Properties of the Conditional Independence Relation},
     journal = {Ann. Probab.},
     volume = {13},
     number = {4},
     year = {1985},
     pages = { 934-945},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992915}
}

van Putten, C.; van Schuppen, J. H. Invariance Properties of the Conditional Independence Relation. Ann. Probab., Tome 13 (1985) no. 4, pp.  934-945. http://gdmltest.u-ga.fr/item/1176992915/