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Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion
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  • Published: March 1994

Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion

  • Ph. Carmona1,
  • F. Petit1 &
  • M. Yor1 

Probability Theory and Related Fields volume 100, pages 1–29 (1994)Cite this article

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  • 33 Citations

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Summary

The scaling property of Brownian motion is exploited systematically in order to extend Paul Lévy's arc sine law to Brownian motion perturbed by its local time at 0. Other important ingredients of the proofs are some Ray-Knight theorems for local times.

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Authors and Affiliations

  1. Laboratoire de Probabilités associé au C.N.R.S. No 224, Université Paris VI, 4, Place Jussieu, Tour 56, 3ème Etage, F-75252, Paris 05, France

    Ph. Carmona, F. Petit & M. Yor

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  1. Ph. Carmona
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  2. F. Petit
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  3. M. Yor
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Carmona, P., Petit, F. & Yor, M. Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion. Probab. Th. Rel. Fields 100, 1–29 (1994). https://doi.org/10.1007/BF01204951

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  • Received: 09 November 1993

  • Revised: 29 March 1994

  • Issue Date: March 1994

  • DOI: https://doi.org/10.1007/BF01204951

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Mathematics Subject Classification

  • 60J55
  • 60J65
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