A Generalization of Multifractional Brownian Motion

被引：1

作者：

Gupta, Neha ^{[1
]}

Kumar, Arun ^{[1
]}

Leonenko, Nikolai ^{[2
]}

机构：

[1] Indian Inst Technol Ropar, Dept Math, Rupnagar 140001, India

[2] Cardiff Univ, Cardiff Sch Math, Senghennydd Rd, Cardiff CF24 4AG, Wales

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

multifractional Brownian motion; long range dependence; harmonizable representation; Hurst parameter; Holder continuity; FRACTIONAL STABLE MOTION;

D O I：

10.3390/fractalfract6020074

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, some properties of multifractional Brownian motion (MFBM) are discussed. It is shown that it has persistence of signs long range dependence (LRD) and persistence of magnitudes LRD properties. A generalization called here nth order multifractional Brownian motion (n-MFBM) that allows to take the functional parameter <mml:semantics>H(t)</mml:semantics> values in the range <mml:semantics>(n-1,n)</mml:semantics> is discussed. Two representations of the n-MFBM are given and their relationship with each other is obtained.

引用

页数：11

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