Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean

다국어 초록 (Multilingual Abstract)

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.

참고문헌 (Reference)

1 Hamilton, J. D., "Time Series Analysis" Princeton University Press 1994

2 Kloeden, P., "The pathwise convergence of approximation schemes for stochastic differential equations" 10 : 235-253, 2007

3 Nualart, D., "The Malliavin Calculus and Related Topics" Springer-Verlag 2006

4 Alos, E., "Stochastic calculus with respect to Gaussian processes" 766-801, 2001

5 El Onsy, B., "Statistical analysis of the non-ergodic fractional Ornstein–Uhlenbeck process of the second kind" 2017

6 Kleptsyna, M., "Statistical analysis of the fractional Ornstein–Uhlenbeck type process" 5 : 229-241, 2002

7 Brouste, A., "Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package" 28 (28): 1529-1547, 2012

8 Tommi Sottinen, "Parameter estimation for the Langevin equation with stationary-increment Gaussian noise" Springer Nature 2017

9 Hu, Y., "Parameter estimation for fractional Ornstein Uhlenbeck processes" 80 : 1030-1038, 2010

10 Azmoodeh, E., "Parameter estimation based on discrete observations of fractional Ornstein–Uhlenbeck process of the second kind" 18 (18): 205-227, 2015

11 El Onsy, B., "Parameter Estimation for Ornstein–Uhlenbeck driven by fractional Ornstein–Uhlenbeck processes" 89 (89): 431-468, 2017

12 Es-Sebaiy, K., "Optimal rates for parameter estimation of stationary Gaussian processes"

13 Es-Sebaiy, K., "On drift estimation for discretely observed non-ergodic fractional Ornstein–Uhlenbeck processes with discrete observations" 9 : 615-625, 2014

14 Kaarakka, T., "On Fractional Ornstein–Uhlenbeck process" 5 : 121-133, 2011

15 Hu, Y., "Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart" Springer 427-442, 2013

16 Mohamed El Machkouri, "Least squares estimator for non-ergodic Ornstein–Uhlenbeck processes driven by Gaussian processes" 한국통계학회 45 (45): 329-341, 2016

17 Peccati, G., "Gaussian Limits for Vector-Valued Multiple Stochastic Integrals" 38 : 247-262, 2005

18 Peccati, G., "Gaussian Approximations of Multiple Integrals" 12 : 350-364, 2007

19 Cheridito, P., "Fractional Ornstein–Uhlenbeck processes" 8 : 1-14, 2003

20 Dehling, H., "Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean" 1-14, 2016

21 Ehsan Azmoodeh, "Drift parameter estimation for fractional Ornstein–Uhlenbeck process of the second kind" Informa UK Limited 49 (49): 1-18, 2014

22 Nourdin, I., "Cambridge Tracts in Mathematics. Normal Approximations with Malliavin Calculus: From Stein’s Method To Universality" Cambridge University 2012