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A new example of ‘independence’ and ‘white noise’
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  • Published: June 1990

A new example of ‘independence’ and ‘white noise’

  • Roland Speicher1 

Probability Theory and Related Fields volume 84, pages 141–159 (1990)Cite this article

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Summary

We examine the notion of ‘free independence’ according to Voiculescu. This form of independence is used for defining ‘free white noise’ or ‘process with stationary and freely independent increments’. We prove a general limit theorem giving the combinatorics of infinitely freely divisible states and thus of free white noises with the help of ‘admissible’ partitions. We realize the free analogues of the Wiener process and of the Poisson process as processes on the full Fock space ofL 2 (—).

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900, Heidelberg, Germany

    Roland Speicher

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  1. Roland Speicher
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Speicher, R. A new example of ‘independence’ and ‘white noise’. Probab. Th. Rel. Fields 84, 141–159 (1990). https://doi.org/10.1007/BF01197843

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  • Received: 04 August 1989

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01197843

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Keywords

  • Stochastic Process
  • White Noise
  • Probability Theory
  • Limit Theorem
  • Poisson Process
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