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A nonstandard construction of Lévy Brownian motion
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  • Published: September 1986

A nonstandard construction of Lévy Brownian motion

  • Andreas Stoll1 

Probability Theory and Related Fields volume 71, pages 321–334 (1986)Cite this article

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  • 8 Citations

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Summary

A nonstandard construction of Lévy Brownian motion on ℝd is presented, which extends R.M. Anderson's nonstandard representation of Brownian motion. It involves a nonstandard construction of white noise and gives as a classical corollary a new white noise integral representation of Lévy Brownian motion. Moreover, a new invariance principle can be deduced in a similar way as Donsker's invariance principles follows from Anderson's construction.

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Authors and Affiliations

  1. Abteilung für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, D-4630, Bochum 1, Federal Republic of Germany

    Andreas Stoll

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  1. Andreas Stoll
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Stoll, A. A nonstandard construction of Lévy Brownian motion. Probab. Th. Rel. Fields 71, 321–334 (1986). https://doi.org/10.1007/BF01000208

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  • Received: 26 March 1984

  • Revised: 15 May 1985

  • Issue Date: September 1986

  • DOI: https://doi.org/10.1007/BF01000208

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Keywords

  • Stochastic Process
  • Brownian Motion
  • White Noise
  • Probability Theory
  • Integral Representation
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