The principle of maximum entropy has been used to analyze the stability of the resulting process observed during the interaction of a random process with a 1/f spectrum and a deterministic action in lumped and distributed systems of nonlinear stochastic differential equations describing the...

We investigate arbitrary stochastic partial differential equations subject to translation invariant and temporally white noise correlations from a nonperturbative framework. The method that we expose first casts the stochastic equations into a functional integral form, then it makes use of the...

We present the results of experimental study of an intensive source of wide-band 1/f noise whose generation appears in a system of two interacting nonequilibrium phase transitions. Such a process has been realized in the region of superposition of a superconductor–normal conductor phase...

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...

A crystal surface, which in equilibrium shows a thermal roughening transition, may roughen, under growth conditions, beneath the equilibrium transition temperature. After discussing a simple nucleation approach, this topic is treated from a point of view based on the Chui–Weeks stochastic...

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a...

An analysis of master–slave hierarchy has been made in a system of nonlinear stochastic equations describing fluctuations with a 1/f spectrum at coupled nonequilibrium phase transitions. It is shown that for a system of stochastic equations there exist different probability distribution...

A formal theory of finding a nonlinear stochastic diffusion equation for density fluctuations in a suspension of colloidal hard spheres, which enables us to study the influence of solvent-mediated hydrodynamic interactions between particles as well as the direct interactions, is presented with...

We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity...

We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal...