Browsing Matematisk institutt by Author "Galimberti, Luca"

Now showing items 1-5 of 5

  • Global existence of dissipative solutions to the Camassa--Holm equation with transport noise 
    Galimberti, Luca; Holden, Helge; Karlsen, Kenneth Aksel Hvistendahl; Pang, Ho Cheung (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 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 (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2023)
    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. (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2021)
  • Stochastic integrals and Gelfand integration in Fréchet spaces 
    Benth, Fred Espen; Galimberti, Luca (Journal article / Tidsskriftartikkel / AcceptedVersion; 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 ...
  • Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds 
    Galimberti, Luca; Karlsen, Kenneth Hvistendahl (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)
    We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Itô) noise. The Cauchy problem defined on a Riemanian manifold is shown to be well-posed. We prove existence of generalized ...