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 分形布朗运动建模中的误差分析 Alternative Title Error Assessment in Modeling with Fractal Brownian Motions liusiming 2013 Source Publication FRACTALS Volume 21Issue:4Pages:1-6 Other Abstract To model a given time series $F(t)$ with fractal Brownian motions (fBms), it is necessary to have appropriate error assessment for related quantities. Usually the fractal dimension $D$ is derived from the Hurst exponent $H$ via the relation $D=2-H$, and the Hurst exponent can be evaluated by analyzing the dependence of the rescaled range $\langle|F(t+\tau)-F(t)|\rangle$ on the time span $\tau$. For fBms, the error of the rescaled range not only depends on data sampling but also varies with $H$ due to the presence of long term memory. This error for a given time series then can not be assessed without knowing the fractal dimension. We carry out extensive numerical simulations to explore the error of rescaled range of fBms and find that for \$0 Subject Area 天文和天体物理 Document Type 期刊论文 Identifier http://libir.pmo.ac.cn/handle/332002/10085 Collection PMO中文期刊 Corresponding Author liusiming Recommended CitationGB/T 7714 liusiming. 分形布朗运动建模中的误差分析[J]. FRACTALS,2013,21(4):1-6. APA liusiming.(2013).分形布朗运动建模中的误差分析.FRACTALS,21(4),1-6. MLA liusiming."分形布朗运动建模中的误差分析".FRACTALS 21.4(2013):1-6.
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