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A Large Deviations Principle Related to the Strong Arc-Sine Law

Author

Listed:
  • Alain Rouault

    (LAMA, Université de Versailles)

  • Marc Yor

    (Université Paris 6, Site Chevaleret)

  • Marguerite Zani

    (Université des Sciences et Technologies de Lille U.F.R. de Mathématiques, Bât)

Abstract

We show a large deviations principle for the family of random variables $$\{ \frac{1}{t}\int_0^t 1 _{B_u } >0du\} $$ when t→+∞, where B=(B u ,u≥0) is a standard linear Brownian motion.

Suggested Citation

  • Alain Rouault & Marc Yor & Marguerite Zani, 2002. "A Large Deviations Principle Related to the Strong Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 15(3), pages 793-815, July.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:3:d:10.1023_a:1016280117892
    DOI: 10.1023/A:1016280117892
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    References listed on IDEAS

    as
    1. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    2. Matthias K. Heck, 1999. "Principles of Large Deviations for the Empirical Processes of the Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 12(1), pages 147-179, January.
    3. Heck, Matthias K., 1998. "The principle of large deviations for the almost everywhere central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 61-75, August.
    4. Peter March & Timo Seppäläinen, 1997. "Large Deviations from the Almost Everywhere Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 10(4), pages 935-965, October.
    Full references (including those not matched with items on IDEAS)

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