The continuum percolation system is developed to model a random stock price process in this work. Recent empirical research has demonstrated various statistical features of stock price changes, the financial model aiming at understanding price fluctuations needs to define a mechanism for the...

The Bak–Sneppen model of co-evolution is used to derive synthetic time series with a priori specified fractal dimension (or Hurst exponent) through a mixing of processes in various lattice dimensions. Both theoretical and numerical analyses concern the avalanches at the critical threshold and...

In this paper we introduce a fractional stochastic version of the Mackey–Glass model which is a potential candidate to model objects in biology and finance. By a semi-martingale approximate approach we find an semi-analytical expression for the solution.

In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian...

Two popular estimators of multifractal properties: the Wavelet Transform Modulus Maxima method and Multifractal Detrended Fluctuation Analysis are applied to investigate signals consisting of normal RR-series in 39 healthy subjects and 90 patients suffering from systolic dysfunction of the left...

A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [1/2,1) is established with transaction costs. In particular, for H∈(1/2,1) the minimal price Cmin(t,St) of an option under transaction costs is obtained, which displays that the timestep...

We show by explicit closed form calculations that a Hurst exponent H≠12 does not necessarily imply long time correlations like those found in fractional Brownian motion (fBm). We construct a large set of scaling solutions of Fokker–Planck partial differential equations (pdes) where H≠12....

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since...

In this work, we analyze two important stochastic processes, the fractional Brownian motion and fractional Gaussian noise, within the framework of the Tsallis permutation entropy. This entropic measure, evaluated after using the Bandt & Pompe method to extract the associated probability...

The length of minimal and maximal blocks equally distant on log–log scale versus fluctuation function considerably influences bias and variance of DFA. Through a number of extensive Monte Carlo simulations and different fractional Brownian motion/fractional Gaussian noise generators, we found...