Random non-linear wave equations: Smoothness of the solutions

Rene Carmona, David Nualart

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)469-508
Number of pages40
JournalProbability Theory and Related Fields
Issue number4
StatePublished - Nov 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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