New type of Brownian motion. (English) Zbl 1235.82053

Gitterman, M.

J. Stat. Phys. 146, No. 1, 239-243 (2012).

Summary: We consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for some random time after the collision (Brownian motion with adhesion for a harmonically bound particle). This is another form of stochastic oscillator, different from the oscillators usually studied which are subject to a random force or having random frequency or random damping. Calculation of the first two stationary moments shows that for white multiplicative noise of week strength the second moment coincides with that of usual Brownian motion, but for symmetric dichotomous noise, the second moment may appear the same type of the “energetic” instability, which exists for white noise random frequency or damping coefficient.

MSC:

82C31	Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
60J65	Brownian motion

Keywords:

stochastic oscillator; random mass; steady-state moments

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