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Статья

Statistical Skorohod embedding problem: Optimality and asymptotic normality

Statistics and Probability Letters. 2015. Vol. 104. P. 169-180.
Belomestny D., Schoenmakers J.

Given a Brownian motion B, 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 BT. We propose a consistent estimator for the density of T, derive its convergence rates and prove their optimality.