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arXiv · 2605.19978

Analytical Approach to Continuous-Time Causal Optimal Transport

Julio Backhoff·Erhan Bayraktar·Ibrahim Ekren·Antonios Zitridis
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Abstract

We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional law given the observation of the target, we characterize the value of this transport problem through a fully nonlinear parabolic master equation on an enlarged state space. We further show that this value coincides with those of two equivalent stochastic control problems on the simplex: a control of the Kushner--Stratonovich filtering equation with a zero-mean condition, and a state-constrained stochastic optimal control problem. Both formulations give rise to implementable numerical schemes that approximate the value from above and below.

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Julio Backhoff, Erhan Bayraktar, Ibrahim Ekren, Antonios Zitridis. 2026-05-19. Analytical Approach to Continuous-Time Causal Optimal Transport. https://arxiv.org/abs/2605.19978

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