Statistical Skorohod embedding problem and its generalizations
- Belomestny, Denis
- Schoenmakers, John G. M.
2010 Mathematics Subject Classification
- 62F10 62J12
- Skorohod embedding problem, Levy process, Mellin transform, Laplace transform, variance mixture models, time-changed Levy processes
Given 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 L(T). 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 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.
- Stochastic Process. Appl., Vol. 126, 7, (2016) pp. 2092--2122 under the new title: Statistical inference for time-changed Lévy processes via Mellin transform approach.