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 dX(t) = theta(t)X(t)dt + epsilon d (W) over tilde H-t, X-0 = x(0), 0 <= t <= T where {(W) over tilde (H)(t) , t >= 0} is a mixed fractional Brownian motion with known Hurst index H and study the asymptotic behaviour of the estimator as epsilon -> 0.