@article{Xie2022, 
author = {Huantian Xie and Nenghui Kuang},
title = {Least squares type estimations for discretely observed nonergodic Gaussian Ornstein-Uhlenbeck processes of the second kind},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {1095-1114},
keywords = {nonergodic Gaussian Ornstein-Uhlenbeck processes of the second kind, least squares type estimation, discrete observations, rate consistent},
url = {https://www.sciopen.com/article/10.3934/math.2022065},
doi = {10.3934/math.2022065},
abstract = {We consider the nonergodic Gaussian Ornstein-Uhlenbeck processes of the second kind defined by    d      X    t    =  θ      X    t    d  t  +  d      Y    t          (      1      )        ,  t  ≥  0  ,      X    0    =  0 with an unknown parameter    θ  >  0  , where    d      Y    t          (      1      )        =      e          −      t        d      G                  a                  t                     and    {      G    t    ,  t  ≥  0  } is a mean zero Gaussian process with the self-similar index    γ  ∈  (      1    2    ,  1  ) and        a    t    =  γ      e                  t        γ            . Based on the discrete observations    {      X                  t        i              :      t    i    =  i      Δ    n    ,  i  =  0  ,  1  ,  ⋯  ,  n  }, two least squares type estimators                      θ        ^              n   and                      θ        ~              n   of    θ are constructed and proved to be strongly consistent and rate consistent. We apply our results to the cases such as fractional Brownian motion, sub-fractional Brownian motion, bifractional Brownian motion and sub-bifractional Brownian motion. Moreover, the numerical simulations confirm the theoretical results.}
}