On the increments of some extensions of the fractional Brownian motion

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

Abstract

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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