Stationary Fluctuations Distributions of Brownian Particle Velocity in a Medium with Fluctuating Viscous Friction Coefficient

Brownian motion in the medium with the fluctuating viscous friction coefficient is described. Stationary function of fluctuations distribution of a Brownian particle velocity for a case of Gaussian random variations of a viscous friction coefficient is calculated. It is shown that this function in limiting cases coincides with Cauchy and Maxwell distribution functions. The author deduced the equation for characteristic function of velocity fluctuations of a Brownian particle on exposure to Poisson random process, and also the solution of this equation for a stationary case was found. The distribution function of fluctuations of a Brownian particle velocity and also its first four moments and cumulant were defined at first approximation. Asymmetry and kurtosis of distribution function is calculated. The author established the Kullback’s measure dependence on Poisson process intensity and distribution function kurtosis. It is proposed to define Poisson process intensity by results of long-term measurements of current fluctuations in small volumes of electrolyte.

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