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 $\epsilon \rightarrow 0.$

翻译：本文研究一类满足如下随机微分方程过程的线性乘子函数$\theta(t)$的非参数估计问题：$$dX_t=\theta(t)X_tdt+\epsilon dW_t^{H,K}, X_0=x_0,0\leq t \leq T$$ 其中$\{W_t^{H,K}, t \geq 0\}$是参数已知的双分数布朗运动，其参数满足$H\in (0,1), K\in (0,1]$且$HK\in (\frac{1}{2},1).$ 我们研究了当$\epsilon \rightarrow 0$时，未知函数$\theta(t)$估计量的渐近性质。