  We extend Walsh's theory of martingale measures in order to deal with
hyperbolic stochastic partial differential equations that are second order in
time, such as the wave equation and the beam equation, and driven by spatially
homogeneous Gaussian noise. For such equations, the fundamental solution can be
a distribution in the sense of Schwartz, which appears as an integrand in the
reformulation of the s.p.d.e. as a stochastic integral equation. Our approach
provides an alternative to the Hilbert space integrals of Hilbert-Schmidt
operators. We give several examples, including the beam equation and the wave
equation, with nonlinear multiplicative noise terms.
