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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</sup> 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.
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