10.2168/LMCS-10(4:12)2014
Kjos-Hanssen, Bjørn
Bjørn
Kjos-Hanssen
Nguyen, Paul Kim Long V.
Paul Kim Long V.
Nguyen
Rute, Jason
Jason
Rute
Algorithmic randomness for Doob's martingale convergence theorem in
continuous time
episciences.org
2014
Computer Science - Logic in Computer Science
Mathematics - Logic
Mathematics - Probability
contact@episciences.org
episciences.org
2013-11-11T00:00:00+01:00
2016-11-21T15:22:49+01:00
2014-12-18
eng
Journal article
https://lmcs.episciences.org/978
arXiv:1411.0186
1860-5974
PDF
1
Logical Methods in Computer Science ; Volume 10, Issue 4 ; 1860-5974
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.