We examine possible closed form solutions for the cumulative distribution function for systems where the probability density function can be adequately described by the generalized non-extensive statistics framework. Application to financial time series as a possible Value at Risk technique...

By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche Börse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show...

We analyzed multifractal properties of 5-min stock returns from a period of over two years for 100 highly capitalized American companies. The two sources: fat-tailed probability distributions and non-linear temporal correlations, vitally contribute to the observed multifractal dynamics of the...

We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The Rényi divergence appears as a natural by-product of the...

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-β) oscillator chains with different boundary conditions and numbers of...

We analyze to what extent the emergence of fat-tailed q-Gaussian distributions of daily leverage returns of North American industrial companies that survive default and de-listing between 2006 and 2012 can be described by superstatistics. To this end, we compare mean values of the Tsallis...

2007–2008 US financial crisis adversely affected the stock markets all over the world.  Asian markets also came under pressure and were differently affected. As markets under stress could reveal features that remain hidden under normal conditions, we use MF-DFA technique to investigate the...