Generalization of van Lambalgen's theorem and blind randomness for conditional probabilities
Abstract
Generalization of the Lambalgen's theorem is studied with the notion of Hippocratic (blind) randomness without assuming computability of conditional probabilities. In [Bauwence 2014], a counter-example for the generalization of Lambalgen's theorem is shown when the conditional probability is not computable. In this paper, it is shown that (i) finiteness of martingale for blind randomness, (ii) classification of two blind randomness by likelihood ratio test, (iii) sufficient conditions for the generalization of the Lambalgen's theorem, and (iv) an example that satisfies the Lambalgen's theorem but the conditional probabilities are not computable for all random parameters.
Cite
@article{arxiv.1310.0709,
title = {Generalization of van Lambalgen's theorem and blind randomness for conditional probabilities},
author = {Hayato Takahashi},
journal= {arXiv preprint arXiv:1310.0709},
year = {2015}
}
Comments
The previous version was presented at CCR2013. The current version is submitted to special issue of CCR2013