2014/07/03 by Denis Belomestny, Belomestny, Denis, John Schoenmakers +1
Computer Science · Decision Sciences · Mathematics · #62G08 #62G20 #62G35 #62P20 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.ST #msc:62G08 #msc:62G20 #msc:62G35 #msc:62P20 #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1407.0873
arxiv created 2014/07/03 · openalex publication_date 2014/07/03 · arxiv updated 2014/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given 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 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 Lévy processes.