SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions

Abstract

In this paper, we consider stochastic partial differential equations driven by space-time white noise in high dimensions. We prove, under reasonable conditions, that the law of the solution admits a density with respect to Lebesgue measure. The stability of the equation, as the higher order differential operator tends to zero, is also studied in the paper.

Keywords:

• Malliavin Calculus
• Stochastic partial differential equations
• Semigroups
• Eigenvalues and Eigenvectors
• 60H07
• 60H15
• 60G20
• 60G60