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January 2003 Stable processes have thorns
Krzysztof Burdzy, Tadeusz Kulczycki
Ann. Probab. 31(1): 170-194 (January 2003). DOI: 10.1214/aop/1046294308

Abstract

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 $t \in [s,s+1)$.

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Krzysztof Burdzy. Tadeusz Kulczycki. "Stable processes have thorns." Ann. Probab. 31 (1) 170 - 194, January 2003. https://doi.org/10.1214/aop/1046294308

Information

Published: January 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1019.60035
MathSciNet: MR1959790
Digital Object Identifier: 10.1214/aop/1046294308

Subjects:
Primary: 60G17 , 60G52

Keywords: local properties of trajectories , Symmetric stable process , thorn points , thorns

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 1 • January 2003
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