Markovian extensions and reductions of a family of σ-algebras
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...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000582 |
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| _version_ | 1832561732355096576 |
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| author | Jelena Bulatovic Gill |
| author_facet | Jelena Bulatovic Gill |
| author_sort | Jelena Bulatovic Gill |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cae30970694c48e1b6dd5c000292ffdb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cae30970694c48e1b6dd5c000292ffdb2025-02-03T01:24:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017352352810.1155/S0161171284000582Markovian extensions and reductions of a family of σ-algebrasJelena Bulatovic Gill0Department of Statistics and Probability, Michigan State University, East Lansing 48824, Michigan, USAIn 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.http://dx.doi.org/10.1155/S0161171284000582Markovian family of σ-algebras; equal predictability; stochastic dynamic system; extension and reduction. |
| spellingShingle | Jelena Bulatovic Gill Markovian extensions and reductions of a family of σ-algebras International Journal of Mathematics and Mathematical Sciences Markovian family of σ-algebras; equal predictability; stochastic dynamic system; extension and reduction. |
| title | Markovian extensions and reductions of a family of σ-algebras |
| title_full | Markovian extensions and reductions of a family of σ-algebras |
| title_fullStr | Markovian extensions and reductions of a family of σ-algebras |
| title_full_unstemmed | Markovian extensions and reductions of a family of σ-algebras |
| title_short | Markovian extensions and reductions of a family of σ-algebras |
| title_sort | markovian extensions and reductions of a family of σ algebras |
| topic | Markovian family of σ-algebras; equal predictability; stochastic dynamic system; extension and reduction. |
| url | http://dx.doi.org/10.1155/S0161171284000582 |
| work_keys_str_mv | AT jelenabulatovicgill markovianextensionsandreductionsofafamilyofsalgebras |