Solution theory to Semilinear Hyperbolic Stochastic Partial Differential   Equations with polynomially bounded coefficients
  We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We provide conditions on the initial data and on the stochastic terms, namely, on the associated spectral measure, so that mild solutions exist and are unique in suitably chosen functional classes. More precisely, function-valued solutions are obtained, as well as a regularity result. 
Alessia Ascanelli, Sandro Coriasco and Andr\'e S\"u\ss
math.AP