STATISTICAL INFERENCE FOR MODELS DRIVEN BY n-TH ORDER FRACTIONAL BROWNIAN MOTION

. We consider the following stochastic integral equation X(t) = mu t + sigma integral(t)(0) phi(s)dB(H)(n)(s), t >= 0, where phi is a known function and B-H(n) is the n-th order fractional Brownian motion. We provide explicit maximum likelihood estimators for both mu and sigma(2), then we formulate explicitly a least squares estimator for mu and an estimator for sigma(2) by using power variations method. The consistency and asymptotic normality are established for those estimators when the number of observations or the time horizon is sufficiently large.