Open Access
2025 Adapted optimal transport between Gaussian processes in discrete time
Madhu Gunasingam, Ting-Kam Leonard Wong
Author Affiliations +
Electron. Commun. Probab. 30: 1-14 (2025). DOI: 10.1214/25-ECP654

Abstract

We derive explicitly the adapted 2-Wasserstein distance between 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.

Funding Statement

The research of T.-K. L. Wong is partially supported by an NSERC Discovery Grant (RGPIN-2019-04419).

Acknowledgments

Some preliminary results were presented at the workshop Optimal Transport and Distributional Robustness hosted at the Banff International Research Station. We thank the organizers and participants for their helpful comments. We also thank the anonymous reviewers for their careful reading and suggestions which improved the paper.

Citation

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Madhu Gunasingam. Ting-Kam Leonard Wong. "Adapted optimal transport between Gaussian processes in discrete time." Electron. Commun. Probab. 30 1 - 14, 2025. https://doi.org/10.1214/25-ECP654

Information

Received: 1 May 2024; Accepted: 8 January 2025; Published: 2025
First available in Project Euclid: 17 January 2025

arXiv: 2404.06625
Digital Object Identifier: 10.1214/25-ECP654

Subjects:
Primary: 49Q22 , 60G15
Secondary: 60B10

Keywords: adapted Brenier , Adapted optimal transport , Bures-Wasserstein , Gaussian process , Knothe-Rosenblatt , Wasserstein distance

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