Preprint 2011-27
Jorge Clarke, Ciprian A. Tudor:
Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet
Abstract:
We study a least square estimator for the drift parameter of the fractional Ornstein-Uhlenbeck sheet, which is defined as the solution of a Langevin equation driven by a fractional Brownian sheet with Hurst parameters in the interval (1/2,5/8). Using the properties of multiple Wiener-Ito integrals we prove that the estimator is strongly consistent. In contrast to the one-dimensional case, the estimator is not asymptotically normal.
This preprint gave rise to the following definitive publication(s):
Jorge CLARKE, Ciprian A. TUDOR: Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet. Journal of the Korean Statistical Society, vol. 41, 3, pp. 341-350, (2012).