'American Institute of Mathematical Sciences (AIMS)'
Publication date
01/01/2023
Field of study
Let SH,K={StH,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 {Sh+tH,K​−ShH,K​,t≥0} converges to {BtHK​,t≥0} as h→∞, where {BtHK​,t≥0} is the fractional Brownian motion with Hurst index HK. Moreover, we study the behavior of the noise associated to the sbfBm and limit theorems to SH,K and the behavior of the tangent process of sbfBm