The paper presents the random-variable formalism of the anomalous diffusion processes. The emphasis is on a rigorous presentation of asymptotic behaviour of random walk processes with infinite mean random time intervals between jumps. We elucidate the role of the so-called inverse-time...

We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency...

The question, what information about the system can be derived from short time series of potassium current signal recorded at various voltages, has been posed. The statistical analysis of 4000-point data samples of ionic current in a single channel of the biological membrane is presented. The...

The time series of successive closed- and open-states durations determined for a voltage-dependent big conductance locust potassium channel (BK channel) have been analyzed. The problem of correlation between the states have been discussed by means of the autocorrelation function, Hurst and...

Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating...