Maximum Likelihood Estimation in the Fractional Vasicek Model

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 ∈ (1/2,1). We construct the maximum likelihood estimators for unknown parameters α and β, and prove their consistency and asymptotic normality.

Keywords

• fractional Brownian motion
• fractional Vasicek model
• maximum likelihood estimation
• strong consistency
• asymptotic normality