An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit
Author
Source
Journal of Probability and Statistics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-11-05
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Londoño, Jaime A.. 2017. An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit. Journal of Probability and Statistics،Vol. 2017, no. 2017, pp.1-5.
https://search.emarefa.net/detail/BIM-1186303
Modern Language Association (MLA)
Londoño, Jaime A.. An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit. Journal of Probability and Statistics No. 2017 (2017), pp.1-5.
https://search.emarefa.net/detail/BIM-1186303
American Medical Association (AMA)
Londoño, Jaime A.. An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit. Journal of Probability and Statistics. 2017. Vol. 2017, no. 2017, pp.1-5.
https://search.emarefa.net/detail/BIM-1186303
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186303