利用比率估计多重分形测度和多重分形随机游动的标度函数
Estimating the scaling function of multifractal measures and multifractal random walks using ratios
摘要：
本文证明了Ludeña [Ann. Appl. Probab.]定义的多重分形过程，即多重级联、多重分形随机测度、多重分形随机游动和多重分形分数随机游动的结构函数的偏差缩减估计的中心极限定理。18（2008）1138-1163]。以前的估计的结构函数在文献中考虑严重偏置的对数收敛速率，而这里考虑的估计有一个多项式的收敛速度收敛速率。
英文摘要：
In this paper, we prove central limit theorems for bias reduced estimators of the structure function of several multifractal processes, namely mutiplicative cascades, multifractal random measures, multifractal random walk and multifractal fractional random walk as defined by Ludeña [Ann. Appl. Probab. 18 (2008) 1138-1163]. Previous estimators of the structure functions considered in the literature were severely biased with a logarithmic rate of convergence, whereas the estimators considered here have a polynomial rate of convergence.
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