  We study the strong consistency and asymptotic normality of a least squares
estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck
processes driven by fractional Brownian motion, extending the results of Chen,
Hu, Wang (2017) to the case of Hurst parameter H \in (1/4 , 1/2) and the
results of Hu, Nualart, Zhou (2019) to a two-dimensional case. When H \in (0,
1/4], it is found that the integrand of the estimator is not in the domain of
the standard divergence operator. To facilitate the proofs, we develop a new
inner product formula for functions of bounded variation in the reproducing
kernel Hilbert space of fractional Brownian motion with Hurst parameter H \in
(0, 1/2). This formula is also applied to obtain the second moments of the
so-called {\alpha}-order fractional Brownian motion and the {\alpha}-fractional
bridges with the Hurst parameter H \in (0, 1/2).
