In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with memory. In our models, the waiting time involves Riemann–Liouville fractional derivative or Riemann–Liouville fractional integral....

The multifractal detrended fluctuation analysis and detrending moving average algorithm were introduced in detail and applied to the study of the multifractal characteristics of the normal signals, the atrial premature beat (APB) signals and the premature ventricular contraction (PVC) signals....

We investigate the correlation inequalities and the decay of correlations of stochastic Ising model in a rectangle with side length 2L×K(LlnL)1/2, where K is some positive constant. With different boundary conditions, at inverse temperature ββc or ββc and zero external field, we show some...

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0α1, here dX(τ)=μX(τ)(dτ)2H+σX(τ)dBH(τ), as a model of asset prices, which captures the subdiffusive...

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|−θ, subject to absorbing boundary condition and the conventional initial...

We develop a financial market model using an Ising spin system on a Sierpinski carpet lattice that breaks the equal status of each spin. To study the fluctuation behavior of the financial model, we present numerical research based on Monte Carlo simulation in conjunction with the statistical...

By using the linear approximation method, the laser intensity power spectrum and signal-to-noise ratio (SNR) are calculated for a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We found that stochastic...

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 numerical characterization of DNA sequences provides a quantitative analysis of data on DNA sequences. In this paper, we construct a 12-component vector based on the information theory to characterize DNA sequences. A potential application of the introduced vector to discriminating protein...

Electronic Cardiogram (ECG) data taken from healthy adult subjects are found to characterize multifractality. In order to quantitatively analyze multifractal spectrum, the area of the spectrum is computed. We have a comparison between the spectrum of the young subjects and that of the old ones....