We consider the fractional Vasicek model of the form dXt = (α-βXt)dt +γdBHt , driven by fractional Brownian motion BH with Hurst parameter H ∈ (1/2,1). We construct the maximum likelihood estimators for unknown parameters α and β, and prove their consistency and asymptotic normality.

No abstract

We consider the fractional Vasicek model of the form dXt = (α-βXt)dt + γdBHt, driven by fractional Brownian motion BH with Hurst parameter H ∈ (0,1). We construct three estimators for an unknown parameter θ=(α,β) and prove their strong consistency.

We investigate the fractional Vasicek model described by the stochastic differential equation dXt = (α − βXt) dt + γ dB H t , X0 = x0, driven by the fractional Brownian motion B H with the known Hurst parameter H ∈ (1/2, 1). We study the maximum likelihood estimators for unknown parameters α and β in the non-ergodic case (when β < 0) for arbitrary x0 ∈ R, generalizing the result of Tanaka, Xiao and Yu (2019) for particular x0 = α/β, derive their asymptotic distributions and prove their asymptotic independence.

No abstract