  In [5] was proved the existence of a solution for the stochastic wave
equation driven by a L\'evy noise, which may have infinite $p$-th moments. In
this work, we show the uniqueness of this solution using a compact support
property of the fundamental solution of the wave operator. Furthermore, we
extend this result to a general class of wave equations. Secondly, as a
consequence of the past-light cone property, we show that $p$-th moments of the
solution are bounded up to a certain stopping times that depend on a bounded
region in $\mathbb{R}^d$.
