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On the computability of a construction of Brownian motion†

Published online by Cambridge University Press:  17 May 2013

GEORGE DAVIE  and
WILLEM L. FOUCHÉ
GEORGE DAVIE
Affiliation:
Department of Decision Sciences, School of Economic Sciences, University of South Africa, PO Box 392, 0003 Pretoria, South Africa Email: davieg@unisa.ac.za; fouchwl@gmail.com
WILLEM L. FOUCHÉ
Affiliation:
Department of Decision Sciences, School of Economic Sciences, University of South Africa, PO Box 392, 0003 Pretoria, South Africa Email: davieg@unisa.ac.za; fouchwl@gmail.com
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Abstract

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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Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Issue 6 , December 2013 , pp. 1257 - 1265
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

†

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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