Linear stochastic dynamics with nonlinear fractal properties

Details Linear stochastic dynamics with nonlinear fractal properties Linear stochastic dynamics with nonlinear fractal properties

1997-09-09

arxiv.org/abs/cond-mat/9709101v1

Physica A 250, 295-314 (1998)

Physics

Condensed Matter

Statistical Mechanics

26 pages, Physica A (in press)

Scientific paper

Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications on population dynamics, epidemics, finance and insurance applications with relation to ARCH(1) process, immigration and investment portfolios and the internet. We highlight the common physical mechanism and summarize the main known results. The distribution and statistical properties of the duration of intermittent bursts are also characterized in details.

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