  We consider a class of multiplicative processes which, added with stochastic
reset events, give origin to stationary distributions with power-law tails --
ubiquitous in the statistics of social, economic, and ecological systems. Our
main goal is to provide a series of exact results on the dynamics and
asymptotic behaviour of increasingly complex versions of a basic multiplicative
process with resets, including discrete and continuous-time variants and
several degrees of randomness in the parameters that control the process. In
particular, we show how the power-law distributions are built up as time
elapses, how their moments behave with time, and how their stationary profiles
become quantitatively determined by those parameters. Our discussion emphasizes
the connection with financial systems, but these stochastic processes are also
expected to be fruitful in modeling a wide variety of social and biological
phenomena.
