On the computability of a construction of Brownian motion
George Elder Davie, Willem L. Fouché · Mathematical Structures in Computer Science · 2013
We examine a construction due to Fouché in which a Brownian motion is constructed from an algorithmically random infinite binary sequence. We show that although the construction is provably not computable in the sense of computable analysis, a lower bound for the rate of convergence is computable in any upper bound for the compressibilty of the sequence, making the construction layerwise computable.