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.
A transfer principle for computing the adapted wasserstein distance between stochastic processes
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Adapted optimal transport on filtered Gaussian processes reduces to a constrained Procrustes problem between Cholesky factors, yielding explicit martingale projections and asymptotic equivalence among bicausal couplings.
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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.
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Adapted Optimal Transport between Filtered Gaussian Processes
Adapted optimal transport on filtered Gaussian processes reduces to a constrained Procrustes problem between Cholesky factors, yielding explicit martingale projections and asymptotic equivalence among bicausal couplings.