统计Skorohod嵌入问题及其推广
Statistical Skorohod embedding problem and its generalizations
摘要：
给定一个Lévy过程$L$，我们考虑了基于独立同分布恢复一个独立随机时间$T$分布的所谓统计Skorohod嵌入问题.样本来自$L_{T}.$我们的方法是基于梅林和拉普拉斯变换的真正使用。我们提出了$T,$密度的一个相容估计，导出了它的收敛速度，并证明了它们的最优性.结果表明，收敛速度很大程度上依赖于$T.$的Mellin变换的衰减。我们还考虑了将所得结果应用于方差均值混合模型和时变Lévy过程的统计推断问题。
英文摘要：
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 $L_{T}.$ 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.
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