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On the infinite divisibility of squared Gaussian processes
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  • Published: March 2003

On the infinite divisibility of squared Gaussian processes

  • Nathalie Eisenbaum1 

Probability Theory and Related Fields volume 125, pages 381–392 (2003)Cite this article

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  • 13 Citations

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Abstract.

 We show that fractional Brownian motions with index in (0,1] satisfy a remarkable property: their squares are infinitely divisible. We also prove that a large class of Gaussian processes are sharing this property. This property then allows the construction of two-parameters families of processes having the additivity property of the squared Bessel processes.

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Authors and Affiliations

  1. Laboratoire de Probabilités, UMR 7599, CNRS - Université de Paris VI 4, Place Jussieu, 75252, Paris Cedex 05, France. e-mail: nae@ccr.jussieu.fr, , , , , , FR

    Nathalie Eisenbaum

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  1. Nathalie Eisenbaum
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Additional information

Received: 1 April 2002 / Revised version: 7 September 2002 / Published online: 19 December 2002

Mathematics Subject Classification (2000): 60E07, 60G15, 60J25, 60J55

Key words or phrases: Gaussian processes – Infinite divisibility – Markov processes

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Eisenbaum, N. On the infinite divisibility of squared Gaussian processes. Probab Theory Relat Fields 125, 381–392 (2003). https://doi.org/10.1007/s00440-002-0245-z

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  • Issue Date: March 2003

  • DOI: https://doi.org/10.1007/s00440-002-0245-z

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Keywords

  • Brownian Motion
  • Large Class
  • Gaussian Process
  • Additivity Property
  • Fractional Brownian Motion
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