Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs

2025/07/12 by Rentian Yao, Yao, Rentian, Yeo-Reum Kim +3 · 1 citation
Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2507.09151

openalex publication_date 2025/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time dependent drift term. As the number m of marginal constraints increases, we prove that the solution of the corresponding MSB problem converges to the law of the solution of the SDE at the rate of O(m^-1), in the sense of KL divergence. Our result extends the work of~\citeagarwal2024iterated to the case where the drift of the underlying stochastic process is time-dependent.

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