Arbitrary Truncated Levy Flight: Asymmetrical Truncation and High-Order Correlations

The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically distributed increments in the general case, and high-order correlations have been investigated. The cumulants of an asymmetrically truncated Levy distribution have been found. The behaviors of asymmetrically truncated Levy flight, as a particular case of a random walk, are considered. It is shown that, in the Levy regime, high-order correlations between values of asymmetrically truncated Levy flight exist. The source of high-order correlations is the non-Gaussianity of the increments: the increment skewness generates threefold correlation, and the increment kurtosis generates fourfold correlation.Comment: 19 pages, 1 figure, To be submitted to Physica

Heat capacity of liquids: A hydrodynamic approach

We study autocorrelation functions of energy, heat and entropy densities obtained by molecular dynamics simulations of supercritical Ar and compare them with the predictions of the hydrodynamic theory. It is shown that the predicted by the hydrodynamic theory single-exponential shape of the entropy density autocorrelation functions is perfectly reproduced for small wave numbers by the molecular dynamics simulations and permits the calculation of the wavenumber-dependent specific heat at constant pressure. The estimated wavenumber-dependent specific heats at constant volume and pressure, $C_{v}(k)$ and $C_{p}(k)$, are shown to be in the long-wavelength limit in good agreement with the macroscopic experimental values of $C_{v}$ and $C_{p}$ for the studied thermodynamic points of supercritical Ar.Comment: 8 pages, 5 figure

Stochastic equation for a jumping process with long-time correlations

A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is characterized by the power-law autocorrelation function. Therefore, it can serve as a model of the 1/f noise as well as a model of the stochastic force in the generalized Langevin equation. This equation is solved for the noise correlations 1/t; the resulting velocity distribution has sharply falling tails. The system preserves the memory about the initial condition for a very long time.Comment: 7 pages, 5 Postscript figure

The use of the comprehensive family of distributions for the regime switching ACD framework

In recent methodological work the well known ACD approach, originally introduced by Engle and Russell (1998), has been supplemented by the involvement of an unobservable stochastic process which accompanies the underlying process of durations via a discrete mixture of distributions. The Mixture ACD model, emanating from the specialized proposal of De Luca and Gallo (2004), has proved to be a moderate tool for description of financial duration data. The use of one and the same family of ordinary distributions has been common practice until now. Our contribution incites to use the rich parameterized comprehensive family of distributions which allows for interacting different distributional idiosyncrasies. JEL classification: C41, C22, C25, C51, G14

Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses

We introduce the technique of time-resolved optical gating (TROG) based on dispersive propagation (DP), a new noninterferometric method for characterizing ultrashort optical pulses in amplitude and phase without the need for a short optical gating pulse. TROG is similar to frequency-resolved optical gating except that the role of time and frequency is interchanged. For the DP-TROG geometry, we show that measurements of the autocorrelation trace of the pulse after propagation through a medium with variable dispersion together with a single measurement of its intensity spectrum contain sufficient information to reconstruct the pulse in amplitude and phase. Pulse reconstruction for this DP-TROG geometry works very well even for the case of a nonlinearly chirped double pulse. Compared with other methods, DP-TROG does not introduce an ambiguity in the direction of time for the pulse. Due to its simplicity and improved sensitivity, DP-TROG is expected to be useful in characterizing low-energy pulses

Multifractal and Network Analysis of Phase Transition

Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate how far a system is from a critical threshold. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the fluctuation and geometrical structures of magnetization time series of two-dimensional Ising model around critical point. The Hurst exponent has been confirmed to be a good indicator of phase transition. Increase of the multifractality of the time series have been observed from generalized Hurst exponents and singularity spectrum. Both Long-term correlation and broad probability density function are identified to be the sources of multifractality of time series near critical regime. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties of magnetization time series from complex network perspective. Evolution of the topology quantities such as clustering coefficient, average degree, average shortest path length, density, assortativity and heterogeneity serve as early warnings of phase transition. Those methods and results can provide new insights about analysis of phase transition problems and can be used as early warnings for various complex systems.Comment: 23 pages, 11 figure