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

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