Stochastics theory of log-periodic patterns
arXiv:cond-mat/0012031 · doi:10.1088/0305-4470/33/50/301
Abstract
We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.
LaTeX, 1 ps figure - To appear J. Phys. A: Math & Gen
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