Stable processes have thorns

Burdzy, Krzysztof ; Kulczycki, Tadeusz

Ann. Probab., Tome 31 (2003) no. 1, p. 170-194 / Harvested from Project Euclid

Résumé

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 $s $ such that $X(t)$ remains in $X(s) + \overline{D}(f)$ for all $t \in [s,s+1)$.

Détail

Publié le : 2003-01-14
Classification:  Symmetric stable process,  local properties of trajectories,  thorn points,  thorns,  60G17,  60G52