Limits of sub-bifractional Brownian noises

Abstract

<abstract><p>Let $ S^{H, K} = \{S^{H, K}_t, t\geq 0\} $ be the sub-bifractional Brownian motion (sbfBm) of dimension 1, with indices $ H\in (0, 1) $ and $ K\in (0, 1]. $ We primarily prove that the increment process generated by the sbfBm $ \left\{S^{H, K}_{h+t}-S^{H, K}_h, t\geq 0\right\} $ converges to $ \left\{B^{HK}_t, t\geq 0\right\} $ as $ h\rightarrow \infty $, where $ \left\{B^{HK}_t, t\geq 0\right\} $ 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 $ S^{H, K} $ and the behavior of the tangent process of sbfBm.</p></abstract>