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The ubiquitously observable 1/f noise is mostly Gaussian but sometimes the non-Gaussianity is recognizable, as well. Here we consider stochastic models of 1/f noise based on the linear stochastic differential equations with the very slowly varying coefficients (intensity of the white noise and relaxation rate) or consisting of a superposition of uncorrelated components with different distributions...
Nonextensive statistical mechanics represents a consistent theoretical framework for investigation of complex systems. We propose the nonlinear stochastic differenctial equations yielding q-Gaussian distribution of signal intensity, featured in the nonextensive statistical mechanics. In addition, the proposed equations generate signals with 1/f behavior of the power spectral density. The joint reproduction...
We analyze a mechanism of intermittecy in nonlinear dynamical systems having the invariant subspace and zero transverse Lyapunov exponent. Our model is similar to the on-off intermittency, occurring due the time-dependent forcing of a bifurcation parameter through a bifurcation point but with nonzero transverse Lyapunov exponent. We show that our nonlinear dynamical systems exhibit 1/fβ noise of the...
The special nonlinear stochastic differential equations generating power-law distributed signals and 1/ƒ noise are considered. The models involve the generalized Constant Elasticity of Variance (CEV) process, the Bessel process, the Squared Bessel process, and the Cox-Ingersoll-Ross (CIR) process, which are applied for modeling the financial markets, as well. In the paper, 1/ƒβ behavior of the power...
One of stylized facts emerging from statistical analysis of financial markets is the inverse cubic law for the cumulative distribution of a number of events of trades and of the logarithmic price change. A simple model, based on the point process model of 1/f noise, generating the long-range processes with the inverse cubic cumulative distribution is proposed and analyzed. Main assumptions of the...
Starting from the developed generalized point process model of 1/f noise [B. Kaulakys et al., Phys. Rev. E 71 (2005) 051105] we derive the nonlinear stochastic differential equations for the signal exhibiting 1/fβ noise and 1/xλ distribution density of the signal intensity with different values of β and λ. The processes with 1/fβ are demonstrated by the numerical solution of the derived equations...
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