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On the computability of a construction of Brownian motion


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.

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The research in this paper was supported by the National Research Foundation (NRF) of South Africa and by the European Union grant agreement PIRSES-GA-2011-2011-294962 in Computable Analysis (COMPUTAL).

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
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