Asymptotic Behavior of Weighted Quadratic and Cubic Variations of Fractional Brownian Motion
نویسندگان
چکیده
The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H . In the quadratic (resp. cubic) case, when H < 1/4 (resp. H < 1/6), we show by means of Malliavin calculus that the convergence holds in L toward an explicit limit which only depends on B. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.
منابع مشابه
Asymptotic Behavior of Weighted Quadratic and Cubic Variations of Fractional Brownian Motion by Ivan Nourdin
The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H . In the quadratic (resp. cubic) case, when H < 1/4 (resp. H < 1/6), we show by means of Malliavin calculus that the convergence holds in L2 toward an explicit limit which only depends on B. This result is somewhat surpris...
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