  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.
