Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion

Abstract

Abstract We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.