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 Mathematical notes of NEFU, 2016, Volume 23, Issue 3, Pages 55–69 (Mi svfu31)

Mathematics

Non-random functions and solutions of Langevin-type stochastic differential equations

E. V. Karachanskayaa, A. P. Petrovab

a Far Eastern State Transport University, 47 Seryshev Street, Khabarovsk 680000, Russia
b North-Eastern Federal University, 48 Kulakovskii Street, Yakutsk 677000, Russia

Abstract: We construct a solution of a Langevine-type stochastic differential equation (SDE) with a non-random function depending on its solution. We determine conditions for such non-random function to appear. Using the solution of a homogeneous SDE, we obtain a solution of the generalized Langevine-type SDE by reducing it to a linear one. We construct a stochastic process with non-random modulus in square which is not a solution to an Ito-type SDE.

Keywords: Langevine-type equation, Brownian motion, stochastic differential equation, Ito's formula, deterministic modulus in square for velocity, analytical solution.

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UDC: 519.21

Citation: E. V. Karachanskaya, A. P. Petrova, “Non-random functions and solutions of Langevin-type stochastic differential equations”, Mathematical notes of NEFU, 23:3 (2016), 55–69

Citation in format AMSBIB
\Bibitem{KarPet16} \by E.~V.~Karachanskaya, A.~P.~Petrova \paper Non-random functions and solutions of Langevin-type stochastic differential equations \jour Mathematical notes of NEFU \yr 2016 \vol 23 \issue 3 \pages 55--69 \mathnet{http://mi.mathnet.ru/svfu31} \elib{https://elibrary.ru/item.asp?id=27507491}