Geodesic
Non-random functions and solutions of Langevin-type stochastic differential equations
Matematičeskie zametki SVFU, Tome 23 (2016) no. 3, pp. 55-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : Langevine-type equation, Ito's formula
Keywords: Brownian motion, stochastic differential equation, deterministic modulus in square for velocity, analytical solution. 
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     title = {Non-random functions and solutions of {Langevin-type} stochastic differential equations},
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E. V. Karachanskaya; A. P. Petrova. Non-random functions and solutions of Langevin-type stochastic differential equations. Matematičeskie zametki SVFU, Tome 23 (2016) no. 3, pp. 55-69. http://geodesic.mathdoc.fr/item/SVFU_2016_23_3_a3/

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