An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit

Jaime A. Londoño

Journal of Probability and Statistics, 2017, vol. 2017, 1-5

Abstract:

For a Polish Sample Space with a Borel -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.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/JPS/2017/9139645.pdf (application/pdf)
http://downloads.hindawi.com/journals/JPS/2017/9139645.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:9139645

DOI: 10.1155/2017/9139645

Access Statistics for this article

More articles in Journal of Probability and Statistics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().