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2013 A transience condition for a class of one-dimensional symmetric Lévy processes
Nikola Sandrić
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Electron. Commun. Probab. 18: 1-13 (2013). DOI: 10.1214/ECP.v18-2802

Abstract

In this paper, we give a sufficient condition for the transience for a class of one dimensional symmetric Lévy processes. More precisely, we prove that a one dimensional symmetric Lévy process with the Lévy measure $\nu(dy)=f(y)dy$ or $\nu(\{n\})=p_n$, where the density function $f(y)$ is such that $f(y)>0$ a.e. and the sequence $\{p_n\}_{n\geq1}$ is such that $p_n>0$ for all $n\geq1$, is transient if $$\int_1^{\infty}\frac{dy}{y^{3}f(y)}<\infty\quad\mbox{or}\quad\sum_{n=1}^{\infty}\frac{1}{n^{3}p_n}<\infty.$$ Similarly, we derive an an alogous transience condition for one-dimensional symmetric random walks with continuous and discrete jumps.

Citation

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Nikola Sandrić. "A transience condition for a class of one-dimensional symmetric Lévy processes." Electron. Commun. Probab. 18 1 - 13, 2013. https://doi.org/10.1214/ECP.v18-2802

Information

Accepted: 24 August 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60125
MathSciNet: MR3101636
Digital Object Identifier: 10.1214/ECP.v18-2802

Subjects:
Primary: 60G17
Secondary: 60G50, 60G51

JOURNAL ARTICLE
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