Causal optimal transport value between finite-state Markov source and diffusion target is characterized by a nonlinear parabolic master equation on enlarged state space and shown equivalent to Kushner-Stratonovich filtering control with zero-mean condition and state-constrained control.
Robust optimization in causal models and g-causal normalizing flows.arXiv preprint arXiv:2510.15458,
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Analytical Approach to Continuous-Time Causal Optimal Transport
Causal optimal transport value between finite-state Markov source and diffusion target is characterized by a nonlinear parabolic master equation on enlarged state space and shown equivalent to Kushner-Stratonovich filtering control with zero-mean condition and state-constrained control.