5 problems

Let $(X_t)$ be a process with a rough continuous component having Hurst exponent $H$ and an additive jump component, and consider estimators based on power variations with smaller…

Consider the nonparametric setting in which the jump activity index is state-dependent, written as $\alpha(x)$, and let $h_n$ denote the high-frequency scale used by the estimator.…

Change-point consistency conjecture. With jumps in $(X_t)$, an analogous result holds true under the conditions of Proposition $$ .

Multifractal-change conjecture. The multifractal nature of the GST process will change under these less regularity assumptions on the ground state.

No-killing conjecture. The displayed property should hold without the assumption that $D$ is relatively compact, and in particular for the minimal process $X^0$ on $E$.