  This paper deals with the drift estimation in linear stochastic evolution
equations (with emphasis on linear SPDEs) with additive fractional noise (with
Hurst index ranging from 0 to 1) via least-squares procedure. Since the
least-squares estimator contains stochastic integrals of divergence type, we
address the problem of its pathwise (and robust to observation errors)
evaluation by comparison with the pathwise integral of Stratonovich type and
using its chain-rule property. The resulting pathwise LSE is then defined
implicitly as a solution to a non-linear equation. We study its numerical
properties (existence and uniqueness of the solution) as well as statistical
properties (strong consistency and the speed of its convergence). The
asymptotic properties are obtained assuming fixed time horizon and increasing
number of the observed Fourier modes (space asymptotics). We also conjecture
the asymptotic normality of the pathwise LSE.
