  This paper presents the error analysis of numerical methods on graded meshes
for stochastic Volterra equations with weakly singular kernels. We first prove
a novel regularity estimate for the exact solution via analyzing the associated
convolution structure. This reveals that the exact solution exhibits an initial
singularity in the sense that its H\"older continuous exponent on any
neighborhood of $t=0$ is lower than that on every compact subset of $(0,T]$.
Motivated by the initial singularity, we then construct the Euler--Maruyama
method, fast Euler--Maruyama method, and Milstein method based on graded
meshes. By establishing their pointwise-in-time error estimates, we give the
grading exponents of meshes to attain the optimal uniform-in-time convergence
orders, where the convergence orders improve those of the uniform mesh case.
Numerical experiments are finally reported to confirm the sharpness of
theoretical findings.
