论文标题
回火如何影响布朗分数运动的局部和全球性质？
How does tempering affect the local and global properties of fractional Brownian motion?
论文作者
论文摘要
本文研究了分数布朗运动（FBM）对幂律的平均表示对这种高斯随机过程的某些局部和全球特性的影响的影响。第二种（TFBMII）的回火分数布朗运动（TFBM）和回火的分数布朗运动是为了研究回火的作用而考虑的过程。回火不会改变FBM的局部特性，包括样品路径和p差异，但它对Breuer-Major定理，FBM的第三和第四级累积剂的渐近行为以及最佳的第四刻定理具有很大的影响。
The present paper investigates the effects of tempering the power law kernel of moving average representation of a fractional Brownian motion (fBm) on some local and global properties of this Gaussian stochastic process. Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) are the processes that are considered in order to investigate the role of tempering. Tempering does not change the local properties of fBm including the sample paths and p-variation, but it has a strong impact on the Breuer-Major theorem, asymptotic behavior of the 3rd and 4th cumulants of fBm and the optimal fourth moment theorem.
