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

Abstract

We study the problem of nonparametric estimation of linear multiplier function $\theta t)$ for processes satisfying stochastic differential equations of the type $dX_t=θ(t)X_tdt+\epsilond\bar W_t^H, X_0=x_0, 0\leq t \leq T$ 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 $\epsilon \to 0.$