Abstract
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 -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.
Acknowledgments
The author would like to express his gratitude to Professor Alexander Schied for comments that greatly improved this manuscript.
Citation
Xiyue Han. "A Gladyshev theorem for trifractional Brownian motion and n-th order fractional Brownian motion." Electron. Commun. Probab. 26 1 - 12, 2021. https://doi.org/10.1214/21-ECP422
Information