Let $ B^{a, b}: = \{B_t^{a, b}, t\geq0\} $ be a weighted fractional Brownian motion of parameters $ a > -1 $, $ |b| < 1 $, $ |b| < a+1 $. We consider a least square-type method to estimate the drift parameter $ \theta > 0 $ of the weighted fractional Ornstein-Uhlenbeck process $ X: = \{X_t, t\geq0\} $ defined by $ X_0 = 0; \ dX_t = \theta X_tdt+dB_t^{a, b} $. In this work, we provide least squares-type estimators for $ \theta $ based continuous-time and discrete-time observations of $ X $. The strong consistency and the asymptotic behavior in distribution of the estimators are studied for all $ (a, b) $ such that $ a > -1 $, $ |b| < 1 $, $ |b| < a+1 $. Here we extend the results of [
Citation: Abdulaziz Alsenafi, Mishari Al-Foraih, Khalifa Es-Sebaiy. Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters[J]. AIMS Mathematics, 2021, 6(11): 12780-12794. doi: 10.3934/math.2021738
Let $ B^{a, b}: = \{B_t^{a, b}, t\geq0\} $ be a weighted fractional Brownian motion of parameters $ a > -1 $, $ |b| < 1 $, $ |b| < a+1 $. We consider a least square-type method to estimate the drift parameter $ \theta > 0 $ of the weighted fractional Ornstein-Uhlenbeck process $ X: = \{X_t, t\geq0\} $ defined by $ X_0 = 0; \ dX_t = \theta X_tdt+dB_t^{a, b} $. In this work, we provide least squares-type estimators for $ \theta $ based continuous-time and discrete-time observations of $ X $. The strong consistency and the asymptotic behavior in distribution of the estimators are studied for all $ (a, b) $ such that $ a > -1 $, $ |b| < 1 $, $ |b| < a+1 $. Here we extend the results of [
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Abdulaziz Alsenafi, Mishari Al-Foraih, Khalifa Es-Sebaiy. Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters[J]. AIMS Mathematics, 2021, 6(11): 12780-12794. doi: 10.3934/math.2021738
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