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

Serge Cohen () and Mario Wschebor ()
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Serge Cohen: Université de Toulouse, Université Paul Sabatier
Mario Wschebor: Universidad de la República

Journal of Theoretical Probability, 2010, vol. 23, issue 4, 1204-1226

Abstract: 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.

Keywords: Occupation measure; Fractional Brownian motion; Limit theorem; 60F05; 60G15; 60G18 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0249-z

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