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August, 1985 Invariance Properties of the Conditional Independence Relation
C. van Putten, J. H. van Schuppen
Ann. Probab. 13(3): 934-945 (August, 1985). DOI: 10.1214/aop/1176992915


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.


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C. van Putten. J. H. van Schuppen. "Invariance Properties of the Conditional Independence Relation." Ann. Probab. 13 (3) 934 - 945, August, 1985.


Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0576.60002
MathSciNet: MR799429
Digital Object Identifier: 10.1214/aop/1176992915

Primary: 60A10
Secondary: 60G05 , 62B05 , 62B20 , 93E03

Keywords: $\sigma$-algebraic realization problem , Conditional independence relation , invariance properties , projection operator , stochastic realization problem

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
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