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...

The process of ion transport through a locust potassium channel is described by means of the Fokker–Planck equation (FPE). The deterministic and stochastic components of the process of switching between various conducting states of the channel are expressed by two coefficients, D(1) and D(2),...

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...

In the framework of the one-dimensional fractal time random walk (FTRW) relaxation model, we rigorously show that the frequency domain response takes, in both nonbiased and biased walks, the only possible Cole-Cole form. The underlying reason for this is the specific form of the relaxation...

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...

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...

The conditionally exponential decay (CED) model is used to explain the scaling laws observed in financial data. This approach enables us to identify the distributions of currency exchange rate or economic indices returns (changes) corresponding to the empirical scaling laws. This is illustrated...

We use the Conditionally Exponential Decay (CED) model to explain the scaling behavior in currency exchange (FX) rates. This approach enables us not only to show that FX returns satisfy scaling with an exponent qualitatively different from that of a random walk, but also to identify the...