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题名: ERROR ASSESSMENT IN MODELING WITH FRACTAL BROWNIAN MOTIONS
作者: Qiao, Bingqiang1; Liu SiMing(刘四明)1
刊名: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
出版日期: 2013-09-01
卷号: 21, 期号:3-4
关键词: Fractal Brownian Motion ; Error Assessment ; Hurst Exponent ; Standard Deviation ; Time Series
DOI: 10.1142/S0218348X13500187
文章类型: Article
英文摘要: 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 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 < H < 0.5, vertical bar F(t + tau) - F(t)vertical bar can be treated as independent for time spans without overlap; for 0.5 < H < 1, the long term memory makes vertical bar F(t + tau) - F(t)vertical bar correlated and an approximate method is given to evaluate the error of . The error and fractal dimension can then be determined self-consistently in the modeling of a time series with fBms.
WOS标题词: Science & Technology ; Physical Sciences
类目[WOS]: Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
研究领域[WOS]: Mathematics ; Science & Technology - Other Topics
收录类别: SCI
语种: 英语
WOS记录号: WOS:000329403700004
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内容类型: 期刊论文
URI标识: http://libir.pmo.ac.cn/handle/332002/15512
Appears in Collections:暗物质和空间天文实验室_期刊论文

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作者单位: 1.Chinese Acad Sci, Key Lab Dark Matter & Space Astron, Purple Mt Observ, Nanjing 210008, Jiangsu, Peoples R China
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