We show existence and uniqueness for the solution of a onedimensional wave equation with non-linear random forcing. Then we give sufficient conditions for the solution at a given time and a given point, to have a density and for this density to be smooth. The proof uses the extension of the Malliavin calculus to the two parameters Wiener functionals.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty