Scale-invariant intergalactic dynamics governed by a statistically homogeneous cascade process generically yields multifractal luminosity distributions with highly inhomogeneous realizations (the standard nonfractal and fractal models are special limiting cases). The main obstacles for extending...

In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We investigated quantitatively the calm-time intervals of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index in the 27-year period from...

We present a universal mechanism for the temporal generation of power-law distributions with arbitrary integer-valued exponents.

The unique scaling behavior of financial time series have attracted the research interest of physicists. Variables such as stock returns, share volume, and number of trades have been found to display distributions that are consistent with a power-law tail. We present an overview of recent...

Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality...

Recent empirical evidence based on extensive databases shows that firm size distributions (FSD) vary with the sample. This paper analyses the effect of sample size on the FSD of Spanish manufacturing firms for the years 2001 and 2006. We use a comprehensive dataset that has two measures of firm...

We introduce and study a stochastic growth–collapse model. The growth process is a steady random inflow with stationary, independent, and non-negative increments. Crashes occur according to an arbitrary renewal process, they are geometric, and their magnitudes are random and are governed by an...

We introduce and study an analytic model for physical systems exhibiting growth-collapse and decay-surge evolutionary patterns. We consider a generic system undergoing a smooth deterministic growth/decay evolution, which is occasionally interrupted by abrupt stochastic collapse/surge...

The Central Limit Theorem (CLT) and Extreme Value Theory (EVT) study, respectively, the stochastic limit-laws of sums and maxima of sequences of independent and identically distributed (i.i.d.) random variables via an affine scaling scheme. In this research we study the stochastic limit-laws of...

Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation...