Stochastic multiplicative processes with reset events

Details Stochastic multiplicative processes with reset events Stochastic multiplicative processes with reset events

1999-02-04

arxiv.org/abs/cond-mat/9902068v1

Phys. Rev. E, 59 (1999) 4945

Physics

Condensed Matter

8 pages, 3 figures. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.59.4945

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behaviour. In the boundary between them, the mean value of the relevant variable is time-independent, and the exponent of the stationary distribution equals -2. The addition of diffusion to the system modifies in a non-trivial way the profile of the stationary distribution. Numerical and analytical results are presented.

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