We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition fo...We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.展开更多
Mutually interacting components form complex systems and these components usually have long- range cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature ...Mutually interacting components form complex systems and these components usually have long- range cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders （MF-X-WL）. We test the validity of tile MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions （bFBMs） with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets （returns and volatilities） and online worlds （online numbers of different genders and different societies） and determine intriguing joint multifractal behavior.展开更多
基金supported by NSFC(11101447),supported by NSFC(11201500)
文摘We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.
基金We acknowledge financial support from the National Natural Science Foundation of China （11375064 and 71532009）, the Program for Changjiang Scholars and Innovative Research Team in University （IRT1028）, and the Fundamental Re- search Funds for the Central Universities.
文摘Mutually interacting components form complex systems and these components usually have long- range cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders （MF-X-WL）. We test the validity of tile MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions （bFBMs） with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets （returns and volatilities） and online worlds （online numbers of different genders and different societies） and determine intriguing joint multifractal behavior.
