Correlation and spectral analysis represent the standard tools to study interdependence in statistical data. However, for the stochastic processes with heavy-tailed distributions such that the variance diverges, these tools are inadequate. The heavy-tailed processes are ubiquitous in nature and...

We generalize the Ornstein–Uhlenbeck (OU) process using Doob’s theorem. We relax the Gaussian and stationary conditions, assuming a linear and time-homogeneous process. The proposed generalization retains much of the simplicity of the original stochastic process, while exhibiting a somewhat...

In this work we study the dissipative dynamics of a system of smooth hard spheres with a constant restitution coefficient and small number of particles in the homogeneous cooling regime. We focus on the velocity distribution from simulations in the molecular dynamics approach. The main goal of...

In this work we study the dissipative dynamics of a system of smooth hard spheres with a constant restitution coefficient and small number of particles in the homogeneous cooling regime. We focus on the velocity distribution from simulations in the Molecular Dynamics approach. The main goal of...

In this work a three parameter stochastic process, termed the Gamma-Ornstein–Uhlenbeck process, has been implemented to analyze geophysical data. Such non-Gaussian Ornstein–Uhlenbeck processes offer the possibility of capturing important distributional deviations from Gaussianity and make...

This paper deals with the problem of pricing equity warrants in a mixed fractional Brownian environment. Based on the quasi-conditional expectation and the Fourier transform, we present the pricing model for equity warrants. Moreover, a hybrid intelligent algorithm, which is based on the Genetic...

The quantum Zeno effect is usually discussed in the context of temporal evolution of a quantum state. We investigate its counterpart in the spatial context and present a general criterion for the occurrence of spatial quantum Zeno effect. Furthermore, a parameter-based position-momentum...

Various biological and physiological properties of living tissue can be studied by means of nuclear magnetic resonance techniques. Unfortunately, the basic physics of extracting the relevant information from the solution of Bloch nuclear magnetic resource (NMR) equations to accurately monitor...

Replica trick turns out to be a powerful method to deal with disordered systems. Nevertheless, if several replicas are involved, calculations become technically difficult in the presence of a spontaneous symmetry breaking. Given a Parisi Replica Symmetry Breaking (RSB) scheme, the Fourier...

Many features of natural phenomena can be observed using time records or series of observations. The time records of phenomena such as physiological and economic data or the temperature of a river can display short- and long-term time scales. These signals can also present trends which are an...