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

Huaiqian Li; Bingyao Wu

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arXiv · 2305.01228

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

Huaiqian Li·Bingyao Wu

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Abstract

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 $p\geq1$. 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.

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BibTeX RIS

Huaiqian Li, Bingyao Wu. 2023-05-02. Wasserstein Convergence for Empirical Measures of Subordinated Fractional Brownian Motions on the Flat Torus. https://arxiv.org/abs/2305.01228

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