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

  • Karachanskaya Elena V., Far Eastern State Transport University, 47 Seryshev Street, Khabarovsk 680000, Russia
  • Petrova Alena P., M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42, Kulakovsky St., Yakutsk 677000, Russia
Keywords: Langevine-type equation, Brownian motion, stochastic differential equation, Ito’s formula, deterministic modulus in square for velocity, analytical solution


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.


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How to Cite
Karachanskaya, E. and Petrova, A. (2016) “Non-random functions and solutions of Langevin-type stochastic differential equations”, Mathematical notes of NEFU, 23(3), pp. 55-69. Available at: (Accessed: 22September2020).