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 $\epsilon \rightarrow 0.$
Categories: math.ST stat.TH