Application of the path integral for calculation of simultaneous probability density

M. A. Guzev<sup>ab

a</sup> Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
^b Far Eastern Federal University, Vladivostok

Abstract: Probability density of a random process was calculated for the linear problem of stochastic dynamics. The result obtained was shown to require the definition of the Green's function of the corresponding problem. The formulas were applied for analysis of one-dimensional Langevin equations and of the particle motion under the influence of random external forces in the presence of linear friction.

Key words: stochastic dynamics, probability density, Gaussian processes, path integrals, Langevin equation.

UDC: 539

MSC: Primary 60G15; Secondary 81S40

Received: 14.04.2017

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