International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 523-528
doi:10.1155/S0161171284000582
Markovian extensions and reductions of a family of σ-algebras
Department of Statistics and Probability, Michigan State University, East Lansing 48824, Michigan, USA
Received 7 February 1984
Copyright © 1984 Jelena Bulatovic Gill. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In the first part of this paper different properties of two special realizations of a stochastic dynamic system, as well as relationships between the realization problem and a problem derived from it are investigated. In the second part, solutions of the following two problems (that follow directly from the realization problem) are given: how to find the minimal (resp. maximal) markovlan flow of information (understood as a family of σ-algebras) that contains (resp. is contained in) given output of a system, and is such that each of these two flows of information is equally predictable by the other one.