ON THE STABILITY OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH LINEAR DRIFT

Abstract

The aim of this paper is to prove the equivalence of a stochastic differential equation with linear drift to a stochastic integral equation in an n-dimensional space. The asymptotic p-stability and asymptotic mean square satbility of the trivial random solution for the stochastic differential equation are also investigated by using properties of the Cauchy operator.