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
In this paper,an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion,a fractional Brownian motion B^(H) with the Hurst parameter H>1/2 and a discontinu...In this paper,an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion,a fractional Brownian motion B^(H) with the Hurst parameter H>1/2 and a discontinuous drift was estimated.Under some proper assumptions,we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Ito stochastic calculus.展开更多
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.
文摘In this paper,an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion,a fractional Brownian motion B^(H) with the Hurst parameter H>1/2 and a discontinuous drift was estimated.Under some proper assumptions,we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Ito stochastic calculus.
