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 time

Authors: Bjørn Kjos-Hanssen ; 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.


    Volume: Volume 10, Issue 4
    Published on: December 18, 2014
    Accepted on: June 25, 2015
    Submitted on: November 11, 2013
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,Mathematics - Probability
    Fundings :
      Source : OpenAIRE Research Graph
    • Computability and Probability; Funder: National Science Foundation; Code: 0901020
    • SUPER-M : School and University Partnership for Educational Renewal in Mathematics; Funder: National Science Foundation; Code: 0841223

    1 Document citing this article

    Share

    Consultation statistics

    This page has been seen 1281 times.
    This article's PDF has been downloaded 995 times.