Abstract
AbstractLet \(\{{B}_{H}(t),t \in{\mathbb{R}}^{\}}\) be a fractional Brownian motion with Hurst index 0 < H < 1. Consider the sub-fractional Brownian motion X H defined as follows : $${X}_{H}(t) = \dfrac{{B}_{H}(t) + {B}_{H}(-t)} {\sqrt{2}},t \geq0.$$ We characterize the lower classes of the sup-norm statistic of X H by an integral test.
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