  We study the problem of nonparametric estimation of the linear multiplier
function $\theta(t)$ for processes satisfying stochastic differential equations
of the type $$dX_t=\theta(t)X_tdt+\epsilon dW_t^{H,K}, X_0=x_0,0\leq t \leq T$$
where $\{W_t^{H,K}, t \geq 0\}$ is a bifractional Brownian motion with known
parameters $H\in (0,1), K\in (0,1]$ and $HK\in (\frac{1}{2},1).$ We investigate
the asymptotic behaviour of the estimator of the unknown function $\theta(t)$
as $\epsilon \rightarrow 0.$
