Adapted optimal transport between Gaussian processes in discrete time

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Abstract

We derive explicitly the adapted 2-Wasserstein distance between arbitrary non-degenerate Gaussian distributions on RN 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.

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Gunasingam et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6fdadb6db643587677a4a https://doi.org/https://doi.org/10.48550/arxiv.2404.06625

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