  Let $M$ be a compact Riemannian homogeneous space (e.g. a Euclidean sphere).
We prove existence of a global weak solution of the stochastic wave equation
\mathbf D_t\partial_tu=\sum_{k=1}^d\mathbf
D_{x_k}\partial_{x_k}u+f_u(Du)+g_u(Du)\,\dot W$ in any dimension $d\ge 1$,
where $f$ and $g$ are continuous multilinear mappings and $W$ is a spatially
homogeneous Wiener process on $\mathbb R^d$ with finite spectral measure. A
nonstandard method of constructing weak solutions of SPDEs, that does not rely
on martingale representation theorem, is employed.
