  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.
