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.
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页数：11
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