分数布朗运动的一些扩展的增量

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-02-13 DOI:10.1016/j.spl.2025.110381

Charles El-Nouty

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引用次数: 0

摘要

设{BH(t)，t≥0}为赫斯特指数为0<；H<；1的分数布朗运动。考虑到工艺BH具有固定增量，详细了解小、中、大增量的特性是必不可少的。这种探索扩展到QHASI类，它是一个中心高斯过程的集合。这一类的主要特征是自相似、拟螺旋和近似平稳增量假设。然而，当考虑到先前一些研究中提出的黑洞的新扩展时，对这些增量的分析需要不同的方法。这项调查揭示了在这个扩展框架内增量行为的显著差异。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the increments of some extensions of the fractional Brownian motion

Let

{B_{H} (t), t \geq 0}

be a fractional Brownian motion with Hurst index

0 < H < 1

. Given that the process

B_{H}

has stationary increments, a detailed understanding of the characteristics of small, medium, and large increments is essential. This exploration extends to the QHASI class presented as a collection of centered Gaussian processes. This class is mainly characterized by a self-similarity, a quasi-helix and an approximately stationary increments assumptions. However, the analysis of these increments requires a different approach when considering the new extension of

B_{H}

proposed in some previous research. This investigation reveals significant differences in the behavior of increments within this extended framework.

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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