We consider M-estimation problems, where the target value is determined using a minimizer of an expected functional of a Levy process. With discrete observations from the Levy process, we can produce a "quasi-path" by shuffling increments of the Levy process, we call it a quasi-process. Under a suitable sampling scheme, a quasi-process can converge weakly to the true process according to the properties of the stationary and independent increments. Using this resampling technique, we can estimate objective functionals similar to those estimated using the Monte Carlo simulations, and it is available as a contrast function. The M-estimator based on these quasi-processes can be consistent and asymptotically normal.

翻译：考虑M估计问题，其中目标值由Levy过程期望泛函的极小化确定。利用Levy过程的离散观测值，可通过重组其增量生成"拟路径"，称之为拟过程。在适当的采样方案下，基于平稳独立增量性质，拟过程能够依分布收敛至真实过程。借助这种重采样技术，可估计与蒙特卡洛模拟类似的目标泛函，并将其作为对比函数使用。基于这些拟过程的M估计量具有相合性和渐近正态性。