Computational and Applied Mathematics seminar

Abstract:
In this talk, we consider the stochastic wave and heat equations on the real line and driven by a Gaussian noise which behaves, in the space variable, like a fractional Brownian motion with Hurst index $H\in (0, 1)$. First, we explain how such a noise may be mathematically modeled, and then we define the notion of mild solution to our equations. Secondly, we focus on our main objective: prove that the solution of each of the above equations is continuous in terms of the parameter $H$, with respect to the convergence in law in the space of continuous functions.
This talk is based on a joint work with Luca M. Giordano (Università degli Studi di Milano) and Maria Jolis (UAB).