How to cite item

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

   
@article{ECP2802,
	author = {Nikola Sandrić},
	title = {A transience condition for a class of one-dimensional symmetric Lévy processes},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {18},
	year = {2013},
	keywords = {characteristics of a semimartingale; electrical network; L\'evy measure; L\'evy process; random walk; recurrence; transience},
	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.
},
	pages = {no. 71, 1-13},
	issn = {1083-589X},
	doi = {10.1214/ECP.v18-2802},    
        url = {http://ecp.ejpecp.org/article/view/2802}}