Asymptotic Behavior of Weighted Quadratic Variations of Fractional Brownian Motion: the Critical Case H = 1/4 by Ivan Nourdin
نویسنده
چکیده
We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H = 1/4. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to B.
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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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 surprisi...
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