@article{Kuang2023, 
author = {Nenghui Kuang},
title = {Limits of sub-bifractional Brownian noises},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {3},
pages = {1240-1252},
keywords = {Sub-bifractional Brownian motion, noise, limit theorem},
url = {https://www.sciopen.com/article/10.3934/era.2023063},
doi = {10.3934/era.2023063},
abstract = {Let        S          H      ,      K        =  {      S    t          H      ,      K        ,  t  ≥  0  } be the sub-bifractional Brownian motion (sbfBm) of dimension 1, with indices    H  ∈  (  0  ,  1  ) and    K  ∈  (  0  ,  1  ]  . We primarily prove that the increment process generated by the sbfBm        {                  S                  h          +          t                          H          ,          K                    −              S        h                  H          ,          K                    ,      t      ≥      0        }   converges to        {                  B        t                  H          K                    ,      t      ≥      0        }   as    h  →  ∞, where        {                  B        t                  H          K                    ,      t      ≥      0        }   is the fractional Brownian motion with Hurst index    H  K. Moreover, we study the behavior of the noise associated to the sbfBm and limit theorems to        S          H      ,      K       and the behavior of the tangent process of sbfBm.}
}