Uniqueness for stochastic non-linear wave equations

We prove uniqueness of solutions of the equation utt=Δu+f(u)+g(u)Ẇ,u(0)=u0,ut(0)=v0 on RdRd in the class of processes with paths in H1H1. Here (u0,v0)(u0,v0) is a random variable in H1⊕L2H1⊕L2, WW is a spatially homogeneous Wiener process with finite spectral measure, and ff, gg are locally Lipschitz functions of subcritical growth.