SpeakerAndrea Papini, Chalmers & Göteborgs universitet
,
Abstract
The stochastic heat equation on the sphere driven by additive Lévy random field is approximated by a spectral method in space and forward and backward Euler–Maruyama schemes in time. The spectral approximation is based on a truncation of the series expansion with respect to the spherical harmonic functions. To do so we restrict to square integrable random field and optimal strong convergence rates for a given regularity of the initial condition and two different settings of regularity for the driving noise are derived for the Euler–Maruyama methods. Besides strong convergence, convergence of the expectation and second moment is shown. Weak rates for the spectral approximation are discussed. Numerical simulations confirming the theoretical results are carried out in simple setting.