Algorithmic randomness for Doob's martingale convergence theorem in continuous time
Logic in Computer Science
2015-07-01 v2 Logic
Probability
Abstract
We study Doob's martingale convergence theorem for computable continuous time martingales on Brownian motion, in the context of algorithmic randomness. A characterization of the class of sample points for which the theorem holds is given. Such points are given the name of Doob random points. It is shown that a point is Doob random if its tail is computably random in a certain sense. Moreover, Doob randomness is strictly weaker than computable randomness and is incomparable with Schnorr randomness.
Keywords
Cite
@article{arxiv.1411.0186,
title = {Algorithmic randomness for Doob's martingale convergence theorem in continuous time},
author = {Bjørn Kjos-Hanssen and Paul Kim Long V. Nguyen and Jason Rute},
journal= {arXiv preprint arXiv:1411.0186},
year = {2015}
}