Limit theorems for a quadratic variation of Gaussian processes - Malukas, Raimondas (Nonlinear Analysis: Modelling and Control, 2011)
In the paper a weighted quadratic variation based on a sequence of partitions for a class of Gaussian processes is considered. Conditions on the sequence of partitions and the process are established for the quadratic variation to converge almost surely and for a central limit theorem to be true. Also applications to bifractional and sub-fractional Brownian motion and the estimation of their parameters are provided.