Develops Poisson-based generalized specific entropy on Wiener space for martingale transport, proving weak convergence and establishing compactness, existence, strong duality, and a coupled HJB-FP system for the resulting SEMOT problem.
Computational optimal transport.Foundations and Trends in Machine Learning, 11(5–6):355–607
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Under Ahlfors regularity of exponent β, the minimal energy distance between a measure and its N-point empirical version decays exactly as N to the power -½(1 + q/β) for power kernels with exponent q in (0,2).
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Generalized specific entropy on Wiener space with application to Martingale Optimal Transport
Develops Poisson-based generalized specific entropy on Wiener space for martingale transport, proving weak convergence and establishing compactness, existence, strong duality, and a coupled HJB-FP system for the resulting SEMOT problem.
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Sharp Rates of MMD Empirical Estimation with Power Kernels
Under Ahlfors regularity of exponent β, the minimal energy distance between a measure and its N-point empirical version decays exactly as N to the power -½(1 + q/β) for power kernels with exponent q in (0,2).