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Fluctuation properties of the Langevin equation including a multiplicative,power-law noise and a quadratic potential are discussed. The noise has the Levystable distribution. If this distribution is truncated, the covariance can bederived in the limit of large time; it falls exponentially. Covariance in thestable case, studied for the Cauchy distribution, exhibits a weakly stretchedexponential shape and can be approximated by the simple exponential. Thedependence of that function on system parameters is determined. Then weconsider a dynamics which involves the above process and obey the generalisedLangevin equation, the same as for Gaussian case. The resulting distributionspossess power-law tails - that fall similarly to those for the driving noise -whereas central parts can assume the Gaussian shape. Moreover, a process withthe covariance 1/t at large time is constructed and the corresponding dynamicalequation solved. Diffusion properties of systems for both covariances arediscussed.

Fluctuations in multiplicative systems with jumps