On the relationship between solutions of a class of one-dimensional stochastic differential equations

Abstract

The main purpose of this paper is to explore the relationship between the solutions of a class of stochastic differential equations in the cases with and without external forces. The central idea is to transform the stochastic differential equations into ordinary differential equations in order to simplify the analysis of their solution properties. This transformation is then combined with Itô's formula to estimate the bounds of the first and second moments of the diffusion process described by the considered stochastic differential equations.