On parameter estimation of fractional Ornstein-Uhlenbeck process

We consider a problem of parameter estimation for the fractional Ornstein-Uhlenbeck model given by the stochastic differential equation dX(t) = -theta X(t)dt + dB(t)(H), t >= 0, where theta > 0 is an unknown parameter to be estimated and B-H is a fractional Brownian motion with Hurst parameter H is an element of (0,1). We provide an estimator for theta, and then we study its strong consistency and asymptotic normality. The main tool in our proofs is the paper [I. Nourdin, D. Nualart and G. Peccati, The Breuer-Major theorem in total variation: Improved rates under minimal regularity, Stochastic Process. Appl. 131 2021, 1-20].