In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian and described by the Continuous Time Random Walk model....

In this paper we investigate asymptotic behavior of the tail probability for subordinated self-similar processes with regularly varying tail probability. We show that the tail probability of the one-dimensional distributions and the supremum tail probability are regularly varying with the...

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 study the continuous time random walk theory from financial tick data of the yen–dollar exchange rate transacted at the Japanese financial market. The dynamical behavior of returns and volatilities in this case is particularly treated at the long-time limit. We find that the volatility for...

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations. Analytical expressions related to neutron scattering experiments are presented and analyzed,...

In this paper we present an algorithm to estimate the Hausdorff fractal dimension. The algorithm uses a recursive formula with a fast enough convergence. The accuracy of results is independent on the size, i.e., degree of definition of the fractal set. This fact is particularly useful when...

The fractal dimension of a set in the Euclidean n-space may depend on the applied concept of fractal dimension. Several concepts are considered here, and in a first part, properties are given for sets such that they have the same fractal dimension for all concepts. In particular, self-similar...