Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-Ergodic Case
DOI:
https://doi.org/10.34874/IMIST.PRSM/fsejournal-v1i1.26873Keywords:
Parameter estimation, Non-ergodic fractional Ornstein-Uhlenbeck process, Young integral.Abstract
We consider the parameter estimation problem for the non-ergodic fractional Ornstein- Uhlenbeck process defined as dXt = θXtdt + dBt, t≥ 0, with a parameter θ > 0, where B is a fractional Brownian motion of Hurst index H ∈ ( 1/2 , 1). We study the consistency and the asymptotic distributions of the least squares estimator ?? of θ based on the observation {Xs, s ∈ [0, t]} as t → ∞.
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