Volatility estimation in fractional Ornstein-Uhlenbeck models

In this article, we study the asymptotic behavior of the realized quadratic variation of a process ʃ ^t ₀ u _sdY ⁽¹⁾ _s, where u is a β-Hölder continuous process with β>1-H and Y ⁽¹⁾ _t=ʃ ^t ₀ e ^-sdB ^H _as, where a _t=He ^t/H and B ^H is a fractional Brownian motion with Hurst index H ϵ (0,1) By exploiting the concentration phenomena, we prove almost sure convergence of the quadratic variation, that holds uniformly in time and on the full range H ϵ (0,1) As an application, we construct strongly consistent estimator for the integrated volatility parameter in a model driven by Y ⁽¹⁾.