The paper consists of two parts: (i) the empirical one where the non-linear, long-term autocorrelations present in high-frequency data extracting from the Warsaw Stock Exchange were analyzed and (ii) theoretical one where predictions of our model (Quantitative Finance 3 (2003) 201; Physica A...

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that...

We study a simple molecular model (at a coarse-grain level) as a basis of irreversible heat transfer through a diathermic partition. The partition separates into two adjacent parts a box containing ideal point particles that communicate only through this partition. We provide the basic mechanism...

The one-dimensional Weierstrass walks (WW) model is developed in the framework of the extended (nonseparable) continuous-time random walk (CTRW) formalism [1–12]. The WW model is a lacunary foundation of Lévy walks [6–12] generalized to a nonconstant velocity. This nonconstant velocity is...

Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income) classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker–Planck counterpart, we derived...

The one-dimensional continuous-time Weierstrass flights (CTWF) model is considered in the framework of the nonseparable continuous-time random walks formalism (CTRW). A novel spatio-temporal coupling is introduced by assuming that in each scale the probability density for the flight and for...

We analysed discrete and continuous Weierstrass–Mandelbrot representations of the Lévy flights occasionally interrupted by spatial localizations. We chose the discrete representation to easily detect by Monte Carlo simulation which stochastic quantity could be a candidate for describing the...