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Random sequences in Fréchet spaces

Abstract

This article deals with the generation of arbitrarily distributed sequencesΦ of random variables in a Fréchet space, using sequences ofcanonical random variables (c.r.v.)-i.e., independently uniformly distributed random variables taking real values in the unit interval [0, 1)-orcanonical random digits (c.r.d.)-i.e., independently uniformly distributed random variables taking integer values in some finite interval [0,B−1]. Two main results are established. First, that the members of a sequence of real random variables in [0, 1) are c.r.v. if and only if all the digits of all thebase- B digital representations of the members of the sequence are c.r.d. Secondly, that, given any sequenceΦ of random variables in a Fréchet space, there is a sequenceΨ of functionsψ n(ξ 1,ξ 2, ...,ξ n), forn=1, 2, 3,... (whereξ 1,ξ 2,...,ξ n,... are c.r.v.) which is distributed identically toΦ.

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Halton, J.H. Random sequences in Fréchet spaces. J Sci Comput 6, 61–77 (1991). https://doi.org/10.1007/BF01068125

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Key words

  • Random sequences
  • Fréchet spaces
  • pseudorandom numbers