标题： 关于Lévy测度和copula的非参数推断 显示英文标题

标题： Nonparametric inference on Lévy measures and copulas

摘要： 本文介绍了评估多变量Lévy测度的非参数方法。从一个Lévy过程的$\mathbf{X}$高频观测数据出发，我们构造了其尾积分和Pareto-Lévy copula的估计量，并证明了这些估计量在某些函数空间中的弱收敛性。对于间隔长度为$\Delta_n$的 n 次增量观测，当$k_n=n\Delta_n$时，收敛速度为$k_n^{-1/2}$，这在关于Lévy测度推断方面是自然的。除了对非等距采样方案的扩展外，我们还提供了Pareto-Lévy copula的分析性质，据我们所知，这些性质在文献中尚未提及。最后，我们通过一个小规模模拟研究来评估我们的估计量的表现，并将其应用于真实数据。 显示英文摘要

摘要： In this paper nonparametric methods to assess the multivariate L\'{e}vy measure are introduced. Starting from high-frequency observations of a L\'{e}vy process $\mathbf{X}$, we construct estimators for its tail integrals and the Pareto-L\'{e}vy copula and prove weak convergence of these estimators in certain function spaces. Given n observations of increments over intervals of length $\Delta_n$, the rate of convergence is $k_n^{-1/2}$ for $k_n=n\Delta_n$ which is natural concerning inference on the L\'{e}vy measure. Besides extensions to nonequidistant sampling schemes analytic properties of the Pareto-L\'{e}vy copula which, to the best of our knowledge, have not been mentioned before in the literature are provided as well. We conclude with a short simulation study on the performance of our estimators and apply them to real data.