An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit
For a Polish Sample Space with a Borel σ-field with a surjective measurable transformation, we define an equivalence relation on sample points according to their ergodic limiting averages. We show that this equivalence relation partitions the subset of sample points on measurable invariant subsets,...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2017-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2017/9139645 |
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doaj-3807d166ecc140e783ad1c9bbc07bee32020-11-24T22:37:15ZengHindawi LimitedJournal of Probability and Statistics1687-952X1687-95382017-01-01201710.1155/2017/91396459139645An Approach of Randomness of a Sample Based on Its Weak Ergodic LimitJaime A. Londoño0Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia, Manizales, ColombiaFor a Polish Sample Space with a Borel σ-field with a surjective measurable transformation, we define an equivalence relation on sample points according to their ergodic limiting averages. We show that this equivalence relation partitions the subset of sample points on measurable invariant subsets, where each limiting distribution is the unique ergodic probability measure defined on each set. The results obtained suggest some natural objects for the model of a probabilistic time-invariant phenomenon are uniquely ergodic probability spaces. As a consequence of the results gained in this paper, we propose a notion of randomness that is weaker than recent approaches to Schnorr randomness.http://dx.doi.org/10.1155/2017/9139645 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jaime A. Londoño |
| spellingShingle |
Jaime A. Londoño An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit Journal of Probability and Statistics |
| author_facet |
Jaime A. Londoño |
| author_sort |
Jaime A. Londoño |
| title |
An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit |
| title_short |
An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit |
| title_full |
An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit |
| title_fullStr |
An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit |
| title_full_unstemmed |
An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit |
| title_sort |
approach of randomness of a sample based on its weak ergodic limit |
| publisher |
Hindawi Limited |
| series |
Journal of Probability and Statistics |
| issn |
1687-952X 1687-9538 |
| publishDate |
2017-01-01 |
| description |
For a Polish Sample Space with a Borel σ-field with a surjective measurable transformation, we define an equivalence relation on sample points according to their ergodic limiting averages. We show that this equivalence relation partitions the subset of sample points on measurable invariant subsets, where each limiting distribution is the unique ergodic probability measure defined on each set. The results obtained suggest some natural objects for the model of a probabilistic time-invariant phenomenon are uniquely ergodic probability spaces. As a consequence of the results gained in this paper, we propose a notion of randomness that is weaker than recent approaches to Schnorr randomness. |
| url |
http://dx.doi.org/10.1155/2017/9139645 |
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