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Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean
Salwa Bajja,Khalifa Es-Sebaiy,Lauri Viitasaari 한국통계학회 2017 Journal of the Korean Statistical Society Vol.46 No.4
We first study the drift parameter estimation of the fractional Ornstein–Uhlenbeck process (fOU) with periodic mean for every 1/2 < H < 1. More precisely, we extend the consistency proved in Dehling et al. (2016) for 1/2 < H < 3 /4 to the strong consistency for any 1/2 < H < 1 on the one hand, and on the other, we also discuss the asymptotic normality given in Dehling et al. (2016). In the second main part of the paper, we study the strong consistency and the asymptotic normality of the fOU of the second kind with periodic mean for any 1/2 < H < 1.