This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Belomestny, DenisSchoenmakers, John G.M.2016-03-242019-06-2820142198-5855https://doi.org/10.34657/3239https://oa.tib.eu/renate/handle/123456789/2989Given a Lévy process L, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time T based on i.i.d. sample from LT. Our approach is based on the genuine use of the Mellin and Laplace transforms. We propose consistent estimators for the density of T; derive their conver-gence rates and prove their optimality. It turns out that the convergence rates heavily depend on the decay of the Mellin transform of T. We also consider the application of our results to the problem of statistical inference for variance-mean mixture models and for time-changed Lévy processes.application/pdfeng510Skorohod embedding problemLévy processMellin transformLaplace transformvariance mixture modelstime-changed Lévy processesReport