Solutions of nonlinear stochastic differential equations with 1/ƒ noise power spectrum

Author

Kaulakys, Bronislovas ; Ruseckas, Julius

Author_Institution

Inst. of Theor. Phys. & Astron., Vilnius Univ., Vilnius, Lithuania

fYear

2011

fDate

12-16 June 2011

Firstpage

192

Lastpage

195

Abstract

The special nonlinear stochastic differential equations generating power-law distributed signals and 1/f 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/f^β behavior of the power spectral density is derived directly from the nonlinear stochastic differential equations and the exact solutions for the particular CEV process are presented.

Keywords

1/f noise; differential equations; econophysics; nonlinear equations; stochastic processes; Cox-Ingersoll-Ross process; Squared Bessel process; constant elasticity-of-variance process; financial markets; noise power spectrum; nonlinear stochastic differential equations; power spectral density; power-law distributed signals; Correlation; Differential equations; Eigenvalues and eigenfunctions; Equations; Mathematical model; Noise; Stochastic processes;

fLanguage

English

Publisher

ieee

Conference_Titel

Noise and Fluctuations (ICNF), 2011 21st International Conference on

Conference_Location

Toronto, ON

Print_ISBN

978-1-4577-0189-4

Type

conf

DOI

10.1109/ICNF.2011.5994297

Filename

5994297