| Abstract: |
| The existence and regularity of densities for the supremum of stochastic processes is a classical problem in probability theory. While such questions are well understood for several Gaussian processes, much less is known for nonlinear stochastic partial differential equations. In this talk, I will present joint work with G. Karali, K. Tzirakis, and P. Zoubouloglou establishing the existence of a density for the supremum of solutions to a class of nonlinear SPDEs in one spatial dimension driven by space time white noise. The class includes the nonlinear stochastic heat equation on a bounded domain with Dirichlet or Neumann boundary conditions. The proof relies on Malliavin calculus and a Bouleau Hirsch type criterion adapted to suprema of random fields. |
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