Far Eastern Mathematical Journal

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Application of the path integral for calculation of simultaneous probability density


Guzev M.A.

2017, issue 1, P. 22-29


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.

Keywords:
stochastic dynamics, probability density, Gaussian processes, path integrals, Langevin equation

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References

[1] V.I. Kliatskin, Stokhasticheskie uravneniia glazami fizika (Osnovnye polozheniia, tochnye rezul'taty i asimptoticheskie priblizheniia), Fizmatlit, M., 2001.
[2] A.N. Vasil'ev, Kvantovopolevaia renormgruppa v teorii kriticheskogo povedeniia i stokhasticheskoi dinamike, PIIaF, SPb, 1998.
[3] Carson. C. Chow, Michael A. Buice, «Integral Methods for Stochastic Differential», Equations Journal of Mathematical Neuroscience, 5:8, (2015), 1–35.
[4] C.W. Gardiner, Stochastic methods: A Handbook for the Natural and Social sciences (Springer Series in Synergetics), Springer, Berlin, 2009.
[5] N.G. Van Kampen, Stochastic processes in physics and chemistry, 3rd ed., Elsevier, Amsterdam, 2007.
[6] A.N. Vasil'ev, Funktsional'nye metody v kvantovoi teorii polia i kvantovoi statistike, Izdatel'stvo Leningr. un-ta, Leningrad, 1976.

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