Nonparametric estimation of linear multiplier for processes driven by a Hermite process

We study the problem of nonparametric estimation of the linear multiplier function $\theta (t)$ for processes satisfying stochastic differential equations of the type $$d{X}_t=\theta (t)X_{t}dt+\epsilon d{Z}_t^{q,H},X_0=x_0,0\le t\le T$$ where $\{Z_t^{q,H},t\ge 0\}$ is a Hermite process with known order $q$ and known self-similarity parameter $H\in (\frac{1}{2},1)\mathrm{.}$ We investigate the asymptotic behaviour of the estimator of the unknown function $\theta (t)$ as $\epsilon \to 0.$