  We address the problem of analyticity up to the boundary of solutions to the
Euler equations in the half space. We characterize the rate of decay of the
real-analyticity radius of the solution $u(t)$ in terms of $\exp{\int_{0}^{t}
\Vert \nabla u(s) \Vert_{L^\infty} ds}$, improving the previously known
results. We also prove the persistence of the sub-analytic Gevrey-class
regularity for the Euler equations in a half space, and obtain an explicit rate
of decay of the radius of Gevrey-class regularity.
