• matching problem
• optimal transport
• probability

Optimal matching problem involves both mathematical analysis and probability theory. Among its different formulations we consider the problem of studying the rate of convergence between the occupation measure of a diffusion process taking values on a compact Riemmanian manifold endowed with a measure. The aim of the thesis is to give new insights on the recent results obtained by Feng-Yu Wang and Jie-Xiang Zhu considering the case of a fractional Brownian motion taking values on the d-dimensional flat torus endowed with the Lebesgue measure.