Wasserstein Convergence for Empirical Measures of Subordinated Fractional Brownian Motions on the Flat Torus

We estimate rates of convergence for empirical measures associated with the subordinated fractional Brownian motion to the uniform distribution on the flat torus under the Wasserstein distance ${\mathbb{W}}_p$ for all $p\ge 1$. In particular, our results coincides with recent ones on the diffusion process and the fractional Brownian motion. As an application, we provide similar results for time-discretized subordinated fractional Brownian motions.