Kjos-Hanssen, Bjørn and Nguyen, Paul Kim Long V. and Rute, Jason - Algorithmic randomness for Doob's martingale convergence theorem in continuous time

lmcs:978 - Logical Methods in Computer Science, December 18, 2014, Volume 10, Issue 4
Algorithmic randomness for Doob's martingale convergence theorem in continuous time

Authors: Kjos-Hanssen, Bjørn and Nguyen, Paul Kim Long V. and Rute, Jason

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.


Source : oai:arXiv.org:1411.0186
DOI : 10.2168/LMCS-10(4:12)2014
Volume: Volume 10, Issue 4
Published on: December 18, 2014
Submitted on: June 25, 2015
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,Mathematics - Probability


Share

Browsing statistics

This page has been seen 39 times.
This article's PDF has been downloaded 9 times.