标题： 多边缘随机桥问题解的收敛速率与来自SDE的边缘约束 显示英文标题

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

摘要： 在本文中，我们研究了多边缘Schrodinger桥（MSB）问题，其边缘约束是具有常数扩散系数且具有时间依赖漂移项的随机微分方程（SDE）的边缘分布。 随着边缘约束的数量$m$增加，我们证明了相应MSB问题的解以KL散度的意义收敛到SDE解的分布，收敛速率为$O(m^{-1})$。 我们的结果扩展了~\cite{agarwal2024iterated}的工作，使其适用于底层随机过程的漂移为时间依赖的情况。 显示英文摘要

摘要： 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.