Adapted optimal transport between Gaussian processes in discrete time

Abstract

We derive explicitly the adapted $2$-Wasserstein distance between non-degenerate Gaussian distributions on ${\mathbb{R}}^N$ and characterize the optimal bicausal coupling(s). This leads to an adapted version of the Bures-Wasserstein distance on the space of positive definite matrices.

16 pages, 2 figures. To appear in Electronic Communications in Probability