Stochastic multiplicative processes with reset events

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution fo r the relevant variable, whose exponent depends on the model parameters. Tw o qualitatively different regimes are observed, corresponding to intermitte nt and regular behavior. In the boundary between them, the mean value of th e relevant variable is time independent, and the exponent of the stationary distribution equals -2. The addition of diffusion to the system modifies i n a nontrivial way the profile of the stationary distribution. Numerical an d analytical results are presented. [S1063-651X(99)05305-2].