  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.
