Some Nonlinear Stochastic Cauchy Problems with Generalized Stochastic Processes

We study some nonlinear stochastic Cauchy problems in the framework of the (C,E,P)-algebras. We adapt the definitions to this framework. By means of suitable regularizations, we define associated generalized problems. We use our previous results about the wave equation in canonical form to obtain generalized solutions. We compare the generalized solutions with the classical ones when they exist.