• Global existence of dissipative solutions to the Camassa--Holm equation with transport noise 

      Galimberti, Luca; Holden, Helge; Karlsen, Kenneth Aksel Hvistendahl; Pang, Ho Cheung (Peer reviewed; Journal article, 2023)
      We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa–Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time ...
    • Neural networks in Fréchet spaces 

      Benth, Fred Espen; Detering, Nils; Galimberti, Luca (Peer reviewed; Journal article, 2022)
      We propose a neural network architecture in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fréchet space X ...
    • Renormalization of stochastic continuity equations on Riemannian manifolds 

      Galimberti, Luca; Karlsen, Kenneth H. (Peer reviewed; Journal article, 2021)
    • Stochastic integrals and Gelfand integration in Fréchet spaces 

      Benth, Fred Espen; Galimberti, Luca (Journal article; Peer reviewed, 2022)
      We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the Gelfand integral commutes with linear ...