  In the wild nonabelian Hodge correspondence on curves, filtered Stokes
G-local systems are regarded as the objects on the Betti side. In this paper,
we demonstrate a construction of the moduli space of them, called the Betti
moduli space, and it reduces to the wild character variety when the Betti
weights are trivial. We study some particular examples including Eguch-Hanson
space and the Airy equation together with the corresponding moduli spaces.
Furthermore, we provide a proof of the correspondence among irregular singular
G-connections, Stokes G-local systems, and Stokes G-representations. This
correspondence can be viewed as the G-version of irregular Rieman-Hilbert
correspondence on curves.
