Adapted optimal transport convergence restores weak continuity for conditional dependence measures and delivers O(N^{-1/3}) rates for adapted empirical and rank-based copula estimators.
Bounding adapted Wasserstein metrics.arXiv preprint arXiv:2407.21492
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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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Dependence Measures via Adapted Optimal Transport: Stability and Rates of Convergence
Adapted optimal transport convergence restores weak continuity for conditional dependence measures and delivers O(N^{-1/3}) rates for adapted empirical and rank-based copula estimators.
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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.