• Mathematics
  • Published 2003

Existence of Density for The Solution to the Three-Dimensional Stochastic Wave Equation

@inproceedings{QuerSardanyons2003ExistenceOD,
  title={Existence of Density for The Solution to the Three-Dimensional Stochastic Wave Equation},
  author={Llu{\'i}s Quer-Sardanyons},
  year={2003}
}
We prove existence of density for the real-valued solution to a 3-dimensional stochastic wave equation. The noise is white in time and with a spatially homogeneous correlation whose spectral measure " satisfies that R R3 "(d»)(1 + j»j 2 ) i· < 1, for some · 2 (0; 1 ). Our appoach is based on the mild for- mulation of the equation given by means of Dalang's extended version of Walsh's stochastic integration. We use the tools of Malliavin calculus and a comparison procedure with respect to smooth… CONTINUE READING

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