Small perturbations in a hyperbolic stochastic partial differential equation

We study the existence and properties of the density for the law of the solution to a nonlinear hyperbolic stochastic partial differential equation, driven by a two-parameter white noise. We also analyze the asymptotic behavior of the density for the law of the solution to the equation obtained by perturbing the noise. Under unrestricted Hِrmanderʹs-type conditions on the coefficients, we establish Varadhanʹs estimates.