 Convergence of adapted smoothed empirical measuresSongyan Hou Stochastic Processes and their Applications, 2026, vol. 191, issue C Abstract: The adapted Wasserstein distance (AW-distance) controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the AW-distance are bottlenecked by the failure of empirical measures (Emp) to converge under this distance. Kernel smoothing and adapted projection have been introduced to construct converging substitutes of empirical measures, known respectively as smoothed empirical measures (S-Emp) and adapted empirical measures (A-Emp). However, both approaches have limitations. Specifically, S-Emp lack comprehensive convergence results, whereas A-Emp in practical applications lead to fewer distinct samples compared to standard empirical measures. Keywords: Adapted Wasserstein distance; Wasserstein distance; Empirical measure; Convergence rate; Kernel smoothing (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002194 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2025.104775 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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