Strassen's local law of the iterated logarithm for the generalized
fractional Brownian motion
Strassen's local law of the iterated logarithm for the generalized
fractional Brownian motion
Let $X:=\{X(t)\}_{t\ge0}$ be a generalized fractional Brownian motion: $$ \{X(t)\}_{t\ge0}\overset{d}{=}\left\{ \int_{\mathbb R} \left((t-u)_+^{\alpha}-(-u)_+^{\alpha} \right) |u|^{-\gamma/2} B(du) \right\}_{t\ge0}, $$ with parameters $\gamma \in (0, 1)$ and $\alpha\in \left(-1/2+ \gamma/2, \, 1/2+ \gamma/2 \right)$. This is a self-similar Gaussian process introduced by Pang and Taqqu (2019) as the scaling limit of power-law …