Functional limit theorems for generalized quadratic variations of Gaussian processes

Arnaud Bégyn

Stochastic Processes and their Applications, 2007, vol. 117, issue 12, 1848-1869

Abstract: In this paper, we establish functional convergence theorems for second order quadratic variations of Gaussian processes which admit a singularity function. First, we prove a functional almost sure convergence theorem, and a functional central limit theorem, for the process of second order quadratic variations, and we illustrate these results with the example of the fractional Brownian sheet (FBS). Second, we do the same study for the process of localized second order quadratic variations, and we apply the results to the multifractional Brownian motion (MBM).

Keywords: Almost; sure; convergence; Central; limit; theorem; Fractional; processes; Gaussian; processes; Generalized; quadratic; variations (search for similar items in EconPapers)
Date: 2007
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