  In this paper, we give a sufficient condition for transience for a class of
one-dimensional symmetric L\'evy processes. More precisely, we prove that a
one-dimensional symmetric L\'evy process with the L\'evy 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
$$\int_1^{\infty}\frac{dy}{y^{3}f(y)}<\infty\quad\textrm{or}\quad
\sum_{n=1}^{\infty}\frac{1}{n^{3}p_n}<\infty.$$ Similarly, we derive an
analogous transience condition for one-dimensional symmetric random walks with
continuous and discrete jumps.
