2 problems

Let $M$ be a Markov process independent of an almost surely increasing $alpha$-stable process $\sigma=\{\sigma(t),\ t\in\mathbb{R}_+\}$ with inverse process $\psi$, and define the…

Let $X_n^c$ and $T_n^c$ be scaled coupled processes converging weakly, as $c\to 0$, to a process $(A(t),D(t))$, and let $E(t)$ be the hitting time of $D$. In the heterogeneous sett…