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Nonlinear stochastic differential equations generating signals with 1/fspectrum have been used so far to describe socio-economical systems. In thispaper we consider the motion of a Brownian particle in an inhomogeneousenvironment such that the motion can be described by the equation yielding 1/fspectrum in a broad range of frequencies. The inhomogeneous environment can bea result, for example, of a linear potential affecting the Brownian particletogether with the medium where steady state heat transfer is present due to thedifference of temperatures at the ends of the medium. The correlation ofcollisions between the Brownian particle and the surrounding molecules can leadto the situation where the finite correlation time becomes important, thus wehave investigated the effect of colored noise in our model. Existence ofcolored noise leads to the additional restriction of the diffusion andexponential cut-off of the distribution of particle positions. Narrower powerlaw part in the distribution of the particle positions results in the narrowerrange of frequencies where the spectrum has power law behavior.

Power-law statistics in the velocity fluctuations of Brownian particle in inhomogeneous media and driven by colored noise