Maximum Likelihood Estimation In The Non-Ergodic Fractional Vasicek Model

We investigate the fractional Vasicek model described by the stochastic differential equation dX(t) = (alpha - beta X-t) dt + gamma dB(t)(H), X-0 = x(0), driven by the fractional Brownian motion B-H with the known Hurst parameter H is an element of(1/2, 1). We study the maximum likelihood estimators for unknown parameters alpha and beta in the non-ergodic case (when beta < 0) for arbitrary x(0) is an element of R, generalizing the result of Tanaka, Xiao and Yu (2019) for particular x(0) = alpha/beta, derive their asymptotic distributions and prove their asymptotic independence.