Related papers: Multifractal properties of return time statistics
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
The generating functional is derived for the fluctuation-dissipation relations which result from the unitarity and reversibility of microscopic dynamics and connect various statistical characteristics of many consecutive (continuous)…
Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to…
Far too often are multiparticle final states studied and models tested on merely single-particle spectra and their integrals, the average multiplicities: A multiparticle final state is a non-linear, complex system and the essential…
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…
We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents…
A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
The frequency constitutes a key state variable of electrical power grids. However, as the frequency is subject to several sources of fluctuations, ranging from renewable volatility to demand fluctuations and dispatch, it is strongly…
We investigate the relations holding among generalized dimensions of invariant measures in dynamical systems and similar quantities defined by the scaling of global averages of powers of return times. Because of a heuristic use of Kac…
We derive the extended fluctuation theorems in presence of multiple measurements and feedback, when the system is governed by Hamiltonian dynamics. We use only the forward phase space trajectories in the derivation. However, to obtain an…
The volume fluctuations in statistical mechanics are discussed. First, the volume fluctuations in ensembles with a fixed external pressure, the so called pressure ensembles, are considered. Second, a generalization of the pressure ensembles…
This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
We discuss research done in two important areas of nonequilibrium statistical mechanics: fluctuation dissipation relations and dynamical fluctuations. In equilibrium systems the fluctuation-dissipation theorem gives a simple relation…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…