The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.
Constructive quan- tization: approximation by empirical measures
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General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
Sharp convergence rates and concentration bounds are established for empirical measures of point processes under a newly introduced Wasserstein distance on counting measures.
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Quantitative Stability of the Shadow for Wasserstein Projections and Sample Complexity
The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.
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Convergence rate of the occupation measure of classes of ergodic processes toward their invariant distribution in mean Wasserstein distance
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
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Wasserstein convergence rates for empirical measures of point processes
Sharp convergence rates and concentration bounds are established for empirical measures of point processes under a newly introduced Wasserstein distance on counting measures.