The Lamperti Transform of fractional Brownian motion and related self-similar Gaussian processes.
The Lamperti Transform of fractional Brownian motion and related self-similar Gaussian processes.
复制标题
分数布朗运动的 Lamperti 变换和相关的自相似高斯过程。
DOI：
10.1080/15326349.2014.868735
复制
发表时间：
2014
影响因子：
0.7
通讯作者：
N.-R.
中科院分区：
文献类型：
--
作者：
Matsui;M. and Shieh;N.-R.
本文给出了自相似高斯过程及其指数的Lamperti变换的二阶行为和期望最大增量的结果。由分数布朗运动及其指数驱动的Ornstein-Uhlenbeck过程最近在文献[1]中得到了研究。[]and参考文献[]，其中我们基本上利用了一些特定的属性，例如，fBM的稳定增量。这里，处理的过程是fBM，bi-fBM和sub-fBM;后两个不是固定增量。我们利用自相似高斯过程的分解，并有效地评估每个分解过程的最大值和相关性。我们还讨论了指数平稳过程的随机建模的使用。
We present results on the second order behavior and the expected maximal increments of Lamperti transforms of self-similar Gaussian processes and their exponentials. The Ornstein Uhlenbeck processes driven by fractional Brownian motion (fBM) and its exponentials have been recently studied in Ref.[]and Ref.[], where we essentially make use of some particular properties, e.g., stationary increments of fBM. Here, the treated processes are fBM, bi-fBM, and sub-fBM; the latter two are not of stationary increments. We utilize decompositions of self-similar Gaussian processes and effectively evaluate the maxima and correlations of each decomposed process. We also present discussion on the usage of the exponential stationary processes for stochastic modeling.