Correlation Structure of Time-Changed Generalized Mixed Fractional Brownian Motion

被引:0
|
作者
Mliki, Ezzedine [1 ,2 ]
机构
[1] Imam Abdulrahman Bin Faisal Univ, Coll Sci, Dept Math, POB 1982, Dammam 31441, Saudi Arabia
[2] Imam Abdulrahman Bin Faisal Univ, Basic & Appl Sci Res Ctr, POB 1982, Dammam 31441, Saudi Arabia
关键词
fractional Brownian motion; generalized mixed fractional Brownian motion; long-range dependence; tempered stable subordinator; gamma process; OPTIONS;
D O I
10.3390/fractalfract7080591
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The generalized mixed fractional Brownian motion (gmfBm) is a Gaussian process with stationary increments that exhibits long-range dependence controlled by its Hurst indices. It is defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst indices. In this paper, we investigate the long-time behavior of gmfBm when it is time-changed by a tempered stable subordinator or a gamma process. As a main result, we show that the time-changed process exhibits a long-range dependence property under some conditions on the Hurst indices. The time-changed gmfBm can be used to model natural phenomena that exhibit long-range dependence, even when the underlying process is not itself long-range dependent.
引用
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页数:11
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