A fractional Fourier transform (FrFT) based estimation method is introduced in this paper to analyze the long range dependence (LRD) in time series. The degree of LRD can be characterized by the Hurst parameter. The FrFT-based estimation of Hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. We used fractional Gaussian noises (FGN) which typically...

By using the enlarged BRS transformations we control the gauge parameter dependence of Green functions in the background field gauge. We show that it is unavoidable – also if we consider the local Ward identity – to introduce the normalization gauge parameter ξo, which enters the Green functions of higher orders similarly to the normalization point κ. The dependence of Green functions on ξo is ...

We investigate the sensitive dependence of asymptotic attractors on both initial conditions and parameters in spatio-temporal chaotic dynamical systems. Our models of spatio-temporal systems are globally coupled two-dimensional maps and locally coupled ordinary differential equations. It is found that extreme sensitive dependence occurs commonly in both phase space and parameter space of these ...