Algorithmic randomness for Doob's martingale convergence theorem in   continuous time
  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. 
Bj{\o}rn Kjos-Hanssen (University of Hawaii at Manoa), Paul Kim Long   V. Nguyen (University of Hawaii at Manoa), Jason Rute...
cs.LO math.LO math.PR