Russian Physics Journal

, Volume 52, Issue 2, pp 184–195 | Cite as

Application of integral transforms to a description of the Brownian motion by a non-Markovian random process

  • A. N. MorozovEmail author
  • A. V. Skripkin

The one-dimensional Brownian motion and the Brownian motion of a spherical particle in an infinite medium are described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. A harmonic oscillator in a viscous medium is also considered within the framework of the examined model. It is demonstrated that for rheological models, random dynamic processes are also non-Markovian in character.

Key words

Brownian motion oscillator non-Markovian process rheological models 


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© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.N. E. Bauman Moscow State Technical UniversityMoscowRussia

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