From Hyper Roughness to Jumps as $H\to -1/2$

Eduardo Abi Jaber, Elie Attal, Mathieu Rosenbaum

We investigate the weak limit of the hyper-rough square-root process as the Hurst index $H$ goes to $-1/2$. This limit corresponds to the fractional kernel $t^{H-1/2}$ losing…