论文标题
从莱维过程的高频观察中恢复布朗尼人并跳跃零件
Recovering Brownian and jump parts from high-frequency observations of a Lévy process
论文作者
论文摘要
我们介绍了两种一般的非参数方法，用于从莱维过程的高频观察中恢复布朗的路径和跳跃成分。第一个过程依赖于重新排序的独立采样正常增量，从而避免调谐参数。该方法的功能是布朗分量，可交换结构的存在以及正常经验分位数函数的快速收敛的较小时间占主导地位的结果。第二个过程等于过滤增量并用最终值补偿。它需要精心选择的阈值，在这种情况下，两种方法都产生相同的收敛速率。该速率取决于小型活动，并根据blumenthal-getoor索引给出。最后，我们讨论可能的扩展，包括多维情况，并提供数值插图。
We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high-frequency observations of a Lévy process. The first procedure relies on reordering of independently sampled normal increments and thus avoids tuning parameters. The functionality of this method is a consequence of the small time predominance of the Brownian component, the presence of exchangeable structures, and fast convergence of normal empirical quantile functions. The second procedure amounts to filtering the increments and compensating with the final value. It requires a carefully chosen threshold, in which case both methods yield the same rate of convergence. This rate depends on the small-jump activity and is given in terms of the Blumenthal-Getoor index. Finally, we discuss possible extensions, including the multidimensional case, and provide numerical illustrations.
