Belomestny, DenisSchoenmakers, John2014-10-132014-10-132014-10-13http://hdl.handle.net/2003/3364310.17877/DE290R-15565Given a Levy 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 a consistent estimator for the density of T; derive its convergence 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 Levy processes.enDiscussion Paper / SFB 823;35/2014Skorohod embedding problemtime-changed Levy processesvariance mixture modelsLaplace transformMellin transformLevy process310330620working paper