Intermittency properties for a family of SPDEs driven by a fractional-type noise
In this talk, we will establish intermittency properties for a family of Stochastic Partial Differential Equations driven by a multiplicative Gaussian noise that has similar asymptotic properties as fractional Brownian motion in time and (possibly) some covariance in space. The solutions exhibit similar properties as the solution to the SPDEs driven by (standard) fractional noise, in particular when it comes to moment estimates. Yet our noise allows to work with Walsh integration techniques and can thus be studied with fewer technical tools. We will illustrate in what aspects this noise and the corresponding solutions are similar to regular fractional noise and in what aspects they diff er. Examples include the stochastic heat and wave equations. Acknowledgement: Daniel Conus's research is partially funded by NSF Grant DMS-1513556.