Quantitative control of Wasserstein distance between Brownian motion and the Goldstein--Kac telegraph process

Abstract

In this manuscript, we provide a non-asymptotic process level control between the telegraph process and the Brownian motion with suitable diffusivity constant via a Wasserstein distance with quadratic average cost. In addition, we derive non-asymptotic estimates for the corresponding time average $p$-th moments. The proof relies on coupling techniques such as coin-flip coupling, synchronous coupling and the Komlós--Major--Tusnády coupling.

60 pp

References in corpus (4)

• Ergodicity of the zigzag process
• Donsker's theorem in {Wasserstein}-1 distance
• Multi-state condensation in Berlin-Kac spherical models
• Estimation of local microcanonical averages in two lattice mean-field models using coupling techniques