Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs
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| Format: | Preprint |
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2025
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| _version_ | 1866913938991480832 |
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| author | Yao, Rentian Kim, Young--Heon Schiebinger, Geoffrey |
| author_facet | Yao, Rentian Kim, Young--Heon Schiebinger, Geoffrey |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_09151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs Yao, Rentian Kim, Young--Heon Schiebinger, Geoffrey Probability Statistics Theory 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. |
| title | Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2507.09151 |