论文标题
标准多曲线布朗运动的扩展
An extension of the standard multifractional Brownian motion
论文作者
论文摘要
在本文中，首先，我们概括了双性布朗运动的定义$ b^{h，k}：= \ big（b^{h，k} \ ;; t \；时间索引$ t $，我们用$ b^{h（。），k} $表示这个新过程。 {\ bf关键词：} {高斯进程;自我类似过程；小部分布朗运动；双分歧布朗尼运动；多曲线布朗运动；局部渐近自相似性。}
In this paper, firstly, we generalize the definition of the bifractional Brownian motion $B^{H,K}:=\Big(B^{H,K}\;;\;t\geq 0\Big)$, with parameters $H\in(0,1)$ and $K\in(0,1]$, to the case where $H$ is no longer a constant, but a function $H(.)$ of the time index $t$ of the process. We denote this new process by $B^{H(.),K}$. Secondly, we study its time regularities, the local asymptotic self-similarity and the long-range dependence properties. {\bf Key words:} {Gaussian process; Self similar process; Fractional Brownian motion; Bifractional Brownian motion; Multifractional Brownian motion; Local asymptotic self-similarity.}
