| Abstract: |
| The adapted Wasserstein distance is a distance between stochastic processes. It is defined in terms of an adapted optimal transport problem that takes into account the flow of information in term. We consider (filtered) Gaussian processes for which explicit computations and their geometric properties have recently been developed. In particular, the adapted Wasserstein distance (with $p = 2$) can be expressed explicitly in terms of the Cholesky factors, and can be interpreted in terms of a constrained Procrustes problem. In this Gaussian setting, we discuss various properties of the adapted Wasserstein distance and also study the multi-causal barycenter. |
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