Bjørn Kjos-Hanssen ; Paul Kim Long V. Nguyen ; Jason Rute - 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 - https://doi.org/10.2168/LMCS-10(4:12)2014
Algorithmic randomness for Doob's martingale convergence theorem in continuous timeArticle

Authors: Bjørn Kjos-Hanssen ORCID; Paul Kim Long V. Nguyen ; Jason Rute

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.

https://doi.org/10.2168/LMCS-10(4:12)2014
Source: arXiv.org:1411.0186
Volume: Volume 10, Issue 4
Secondary volumes: Selected Papers of the 10th International Conference on Computability and Complexity in Analysis (CCA 2013)
Published on: December 18, 2014
Imported on: November 11, 2013
Keywords: Computer Science - Logic in Computer Science, Mathematics - Logic, Mathematics - Probability
Licence: arXiv.org - Non-exclusive license to distribute
Funding:
    Source : OpenAIRE Graph
  • SUPER-M : School and University Partnership for Educational Renewal in Mathematics; Funder: National Science Foundation; Code: 0841223
  • Computability and Probability; Funder: National Science Foundation; Code: 0901020

Classifications

Mathematics Subject Classification 20201
Sources:
  • [1] zbMATH Open.

2 Documents citing this article

Share and export

Consultation statistics

This page has been seen 3668 times.
This article's PDF has been downloaded 1567 times.