Statistical skorohod embedding problem and its generalizations
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Date
2014-10-13
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Abstract
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
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.
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Keywords
Skorohod embedding problem, time-changed Levy processes, variance mixture models, Laplace transform, Mellin transform, Levy process