Stable processes have thorns
Stable processes have thorns
Let $X(t)$ be the symmetric $\alpha$-stable process in $\R$, $\alpha \in (0,2)$, $d \ge 2$. For $f\dvtx (0,1) \to (0,\infty)$ let $D(f)$ be the thorn $\{x \in \R\dvtx x_{1} \in (0,1),\allowbreak |(x_{2},\ldots,x_{d})| < f(x_{1})\}$. We give an integral criterion in terms of $f$ for the existence of a random time …