A transience condition for a class of one-dimensional symmetric Lévy processes

Nikola Sandrić (University of Zagreb)

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.


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Pages: 1-13

Publication Date: August 24, 2013

DOI: 10.1214/ECP.v18-2802

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