Modeling scaled processes and clustering of events by the nonlinear stochastic differential equations
B. Kaulakys, M. Alaburda, Vygintas Gontis, Massimo Macucci, Giovanni Basso · AIP conference proceedings · 2009
We present and analyze the nonlinear stochastic differential equations generating scaled signals with the power‐law statistics, including 1/fβ noise and q‐Gaussian distribution. Numerical analysis reveals that the process exhibits some peaks, bursts or extreme events, characterized by power‐law distributions of the burst statistics and, therefore, the model may simulate self‐organized critical and other systems exhibiting avalanches, bursts or clustering of events.