{"ID":2895367,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09151","arxiv_id":"2507.09151","title":"Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs","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~\\cite{agarwal2024iterated} to the case where the drift of the underlying stochastic process is time-dependent.","short_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 tha...","url_abs":"https://arxiv.org/abs/2507.09151","url_pdf":"https://arxiv.org/pdf/2507.09151v1","authors":"[\"Rentian Yao\",\"Young--Heon Kim\",\"Geoffrey Schiebinger\"]","published":"2025-07-12T05:54:54Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}