带跳的分数维Brown 运动幂变差的渐近行为

本文研究了X_t = B^H_t + ξ_t 现实幂变差的渐近理论, B^H 为Hurst 指数为H∈(0,1) 的分数维Brown 运动,ξ为与B^H独立的非Gauss Lévy 过程, 我们给出了其大数定律, 以及经适当中心化的中 心极限定理, 这些结果将为处理具有长期记忆跳过程的统计问题提供理论基础.

Asymptotic properties of power variations for fractional Brownian motion with jumps

In this paper, we study the asymptotic behavior of the realized power variations of processes of the form X_t = B^H_t + ξ_t, where B^H is a fractional Brownian motion with Hurst parameter H∈(0,1), and ξ is a purely non-Gaussian Lévy process and independent of B^H. We prove the convergence in probability for the properly normalized realized power variation and some associated stable central limit theorems. These conclusions provide new statistical tools to consider the long memory processes with jumps.