Nonparametric Estimation of Linear Multiplier for Processes Driven by Mixed fractional Brownian Motion

We study the problem of nonparametric estimation of linear multiplier function $\theta t)$ for processes satisfying stochastic differential equations of the type $d{X}_t=\theta (t)X_{t}dt+\text{epsilond}{\bar{W}}_t^H,X_0=x_0,0\le t\le T$ where $\{{\bar{W}}_T^H,t\ge 0\}$ is a mixed fractional Brownian motion with known Hurst index $H$ and study the asymptotic behaviour of the estimator as $ϵ\to 0.$