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.
The Wasserstein space of stochastic processes in continuous time.arXiv preprint arXiv:2501.14135
3 Pith papers cite this work. Polarity classification is still indexing.
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Adapted Wasserstein barycenters of Gaussian processes decompose into independent classical Bures–Wasserstein problems, but the claimed uniqueness fails for degenerate Gaussian inputs.
Derives a projected McKean-Vlasov SDE whose flow converges to the minimizer of entropic weak optimal transport in adapted Wasserstein space.
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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 Wasserstein Barycenters of Gaussian Processes
Adapted Wasserstein barycenters of Gaussian processes decompose into independent classical Bures–Wasserstein problems, but the claimed uniqueness fails for degenerate Gaussian inputs.
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Projected McKean--Vlasov Dynamics for Entropic Weak Optimal Transport
Derives a projected McKean-Vlasov SDE whose flow converges to the minimizer of entropic weak optimal transport in adapted Wasserstein space.