Parameter Estimation of Complex Fractional Ornstein-Uhlenbeck Processes with Fractional Noise

Abstract

We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart, [Statist. Probab. Lett., 80 (2010), 1030-1038] to a special 2-dimensions. The strategy is to exploit the Garsia-Rodemich-Rumsey inequality and complex fourth moment theorems. The main ingredients of this paper are the sample path regularity of a multiple Wiener-Ito integral and two equivalent conditions of complex fourth moment theorems in terms of the contractions of integral kernels and complex Malliavin derivatives.