Absolute continuity for SPDEs with irregular fundamental solution

作者：Sanz Sole Marta^*; Suess Andre

来源：Electronic Communications in Probability, 2015, 20(0).

DOI：10.1214/ECP.v20-3831

• Stochastic partial differential equations
• stochastic wave equation
• densities

For the class of stochastic partial differential equations studied in [ 2], we prove the existence of density of the probability law of the solution at a given point (t; x), and that the density belongs to some Besov space. The proof relies on the method developed in [ 6]. The result can be applied to the solution of the stochastic wave equation with multiplicative noise, Lipschitz coefficients and any spatial dimension d >= 1, and also to the heat equation. This provides an extension of the results proved in [ 15].

• 出版日期2015-2-14