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.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–74, February, 2009.
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Morozov, A.N., Skripkin, A.V. Application of integral transforms to a description of the Brownian motion by a non-Markovian random process. Russ Phys J 52, 184–195 (2009). https://doi.org/10.1007/s11182-009-9217-4
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DOI: https://doi.org/10.1007/s11182-009-9217-4