Euler-Maruyama approximations of the stochastic heat equation on the sphere
Abstract
The stochastic heat equation on the sphere driven by additive isotropic Wiener noise 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. Optimal strong convergence rates for a given regularity of the initial condition and driving noise are derived for the Euler-Maruyama methods. Besides strong convergence, convergence of the expectation and second moment is shown, where the approximation of the second moment converges with twice the strong rate. Numerical simulations confirm the theoretical results.
Keywords
Cite
@article{arxiv.2307.07564,
title = {Euler-Maruyama approximations of the stochastic heat equation on the sphere},
author = {Annika Lang and Ioanna Motschan-Armen},
journal= {arXiv preprint arXiv:2307.07564},
year = {2024}
}
Comments
Updated convergence plot for the Monte Carlo forward Euler-Maruyama scheme compared to published version