Estimation of all parameters in the fractional Ornstein–Uhlenbeck model under discrete observations

Let the Ornstein–Uhlenbeck process $$(X_t)_{t\ge 0}$$ driven by a fractional Brownian motion $$B^{H }$$ described $$dX_t = -\theta X_t dt + \sigma dB_t^{H be observed at discrete time instants $$t_k=kh$$ , $$k=0, 1, 2, \ldots 2n+2 $$ . We propose an ergodic type statistical estimator $${\hat{\theta }}_n $${\hat{H}}_n and $${\hat{\sigma to estimate all parameters $$\theta H $$\sigma in above model simultaneously. prove strong consistence rate of convergence estimator. The step size h can arbitrarily fixed will not forced go zero, which is usually reality. tools use are generalized moment approach (via theorem) Malliavin calculus.