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On Tightness and Weak Convergence in the Approximation of the Occupation Measure of Fractional Brownian Motion

Author

Listed:
  • Serge Cohen

    (Université de Toulouse, Université Paul Sabatier)

  • Mario Wschebor

    (Universidad de la República)

Abstract

In this paper we consider approximations of the occupation measure of the Fractional Brownian motion by means of some functionals defined on regularizations of the paths. In a previous article Berzin and León proved a cylindrical convergence to a Wiener process of conveniently rescaled functionals. Here we show the tightness of the approximation in the space of continuous functions endowed with the topology of uniform convergence on compact sets. This allows us to simplify the identification of the limit.

Suggested Citation

  • Serge Cohen & Mario Wschebor, 2010. "On Tightness and Weak Convergence in the Approximation of the Occupation Measure of Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1204-1226, December.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:4:d:10.1007_s10959-009-0249-z
    DOI: 10.1007/s10959-009-0249-z
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    References listed on IDEAS

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    1. Chambers, Daniel & Slud, Eric, 1989. "Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 93-107, June.
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