Strong solutions to stochastic wave equations with values in Riemannian manifolds

Let M be a d-dimensional compact Riemannian manifold. We prove existence of a unique global strong solution of the stochastic wave equation Dt ∂tu = Dx∂xu+Yu(∂t u, ∂xu)W˙ , where Y is a C1-smooth transformation and W is a spatially homogeneous Wiener process on R whose spectral measure has finite moments up to order 2. © 2007 Published by Elsevier Inc.