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
    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.

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