Quadratic Variations along Irregular Subdivisions for Gaussian Processes

Arnaud Begyn (Laboratoire de statistiques et probabilites, Université Paul Sabatier, Fra)


In this paper we deal with second order quadratic variations  along general  subdivisions for processes with Gaussian increments. These have almost surely a deterministic limit under conditions on the mesh of the subdivisions. This limit depends on the singularity function of the process and on the structure of the subdivisions too. Then we illustrate the results with the example of the time-space deformed fractional Brownian motion and we present some simulations.

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Pages: 691-717

Publication Date: July 13, 2005

DOI: 10.1214/EJP.v10-245


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