Title : Nonlinear noise excitation and intermittency
We first measure noise excitability for SPDEs in terms of the energy of the solutions. We show that there is a near-dichotomy: " Semidiscrete " equations are nearly always far less excitable than "continuous" equations, and then we identify the reason for this dichotomy.
We also look at more concrete problems such as stochastic heat equations on an interval with Dirichlet and Neumann boundary conditions and then stochastic wave equation on the real line. We show the surprising result that the stochastic heat equation on the interval with Dirichlet boundary condition is significantly more noise excitable than the stochastic wave equation. This is joint work with Davar Khoshnevisan .