On a Class of Stochastic Hyperbolic Equations with Double Characteristics

We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients our operator depend polynomially space variables, while noise is additive, white time and coloured space. provide sufficient condition spectral measure covariance functional describing that allows for existence random field solution resulting stochastic equation. Our approach based explicit computations fundamental its Fourier transform.