Bunched black (and grouped grey) swans: Dissipative and non‐dissipative models of correlated extreme fluctuations in complex geosystems. Issue 2 (31st January 2013) - Watkins, N. W.
Abstract : [1] I review the hierarchy of approaches to complex systems, focusing particularly on stochastic equations. I discuss how the main models advocated by the late Benoit Mandelbrot fit into this classification, and how they continue to contribute to cross‐disciplinary approaches to the increasingly important problems of correlated extreme events and unresolved scales. The ideas have broad importance, with applications ranging across science areas as diverse as the heavy tailed distributions of intense rainfall in hydrology, after which Mandelbrot named the "Noah effect"; the problem of correlated runs of dry summers in climate, after which the "Joseph effect" was named; and the intermittent, bursty, volatility seen in finance and fluid turbulence. Abstract : Mandelbrot's Noah effect, and heavy tailed probability distributions. Mandelbrot's Joseph effect, and long‐range dependence in time. Multiplicative processes and the volatility bunching effect.