Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations

Abstract

We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order structural (height-height correlation) functions. Analytical expressions for such characteristics are derived and the comparison with numerical calculations is presented. The numerical calculations reveal links between the proposed model and models where signals consist of bursts characterized by the power-law distributions of burst size, burst duration and the interburst time, as in a case of avalanches in self-organized critical (SOC) models and the extreme event return times in long-term memory processes. The presented approach may be useful for modeling the long-range scaled processes exhibiting 1/f noise and power-law distributions.

16 pages, 4 figures

References in corpus (16)

• Model for l/f Flux Noise in SQUIDs and Qubits
• Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
• Dangling-bond spin relaxation and magnetic 1/f noise from the amorphous-semiconductor/oxide interface: Theory
• Review of Flicker Noise Spectroscopy in Electrochemistry
• $1/f$ noise and avalanche scaling in plastic deformation
• Spectral fluctuations of billiards with mixed dynamics: from time series to superstatistics
• A model for interevent times with long tails and multifractality in human communications: An application to financial trading
• Self-organised criticality and 1/f noise in single-channel current of voltage-dependent anion channel
• Modeling long-range memory trading activity by stochastic differential equations
• Trading activity as driven Poisson process: comparison with empirical data
• Exact numerical simulation of power-law noises
• Long-range memory model of trading activity and volatility
• Quantum Theory of Flicker Noise in Metal Films
• Quality factor due to roughness scattering of shear horizontal surface acoustic waves in nanoresonators
• Point Process Models of 1/f Noise and Internet Traffic
• Modelling of 1/f noise by sequences of stochastic pulses of different duration

Cited by in corpus (4)

• A long-range memory stochastic model of the return in financial markets
• Intermittency in relation with 1/f noise and stochastic differential equations
• Nonlinear Stochastic Model of Return matching to the data of New York and Vilnius Stock Exchanges
• A general approach for analyzing baseline power spectral densities: Zwanzig-Mori projection operators and the generalized Langevin equation