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arXiv · 1102.5491

Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case

Rachid Belfadli·Khalifa Es-Sebaiy·Youssef Ouknine
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Abstract

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=θX_tdt+dB_t,\ t\geq0$, with a parameter $θ>0$, where $B$ is a fractional Brownian motion of Hurst index $H\in(1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator $\hatθ_t$ of $θ$ based on the observation $\{X_s,\ s\in[0,t]\}$ as $t\rightarrow\infty$.

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Rachid Belfadli, Khalifa Es-Sebaiy, Youssef Ouknine. 2011-02-27. Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case. https://arxiv.org/abs/1102.5491

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