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A Gladyshev theorem for trifractional Brownian motion and $n$-th order fractional Brownian motion
Xiyue Han · 2021-05-06 · via math.PR updates on arXiv.org

We prove limit theorems for the weighted quadratic variation of trifractional Brownian motion and $n$-th order fractional Brownian motion. Furthermore, a sufficient condition for the $L^P$-convergence of the weighted quadratic variation for Gaussian processes is obtained as a byproduct. As an application, we give a statistical estimator for the self-similarity index of trifractional Brownian motion. These theorems extend results of Baxter, Gladyshev, and Norvaiša.

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