  We define a random measure generated by a real anisotropic harmonizable
fractional stable field $Z^H$ with stability parameter $\alpha\in(1,2)$ and
Hurst index $H\in(1/2,1)$ and prove that the measure is $\sigma$-additive in
probability. An integral with respect to this measure is constructed, which
enables us to consider a wave equation in $\mathbb R^3$ with a random source
generated by $Z^H$. We show that the solution to this equation, given by
Kirchhoff's formula, has a modification, which is H\"older continuous of any
order up to $(3H-1)\wedge 1$. In the case where $H\in(2/3,1)$, we show further
that the modification is absolutely continuous.
