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

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

### 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.

### References

Received

15-08-2016

How to Cite

*Mathematical notes of NEFU*, 23(3), pp. 55-69. Available at: http://mzsvfu.ru/index.php/mz/article/view/non-random-functions-and-solutions-of%20langevin-type-stochastic-differential-equations (Accessed: 22September2020).

Issue

Section

Mathematics

This work is licensed under a Creative Commons Attribution 4.0 International License.