THE EXISTENCE AND UNIQUENESS OF THE INVARIANT MEASURE FOR THE SOLUTION OF SDEs WITH NONLINEAR COEFFICIENTS

Abstract

The invariant measure is one of the important properties of stochastic differential equations (SDEs). This problem has been well studied for SDEs with regular coefficients. However, there are many open questions in the case of low regular coefficients or irregular coefficients. One of the important questions is that the conditions of the coefficients lead to the existence and uniqueness of the invariant measure. In this paper, we consider SDEs with low regular coefficients. More precisely, this paper considers SDEs with the super-linear, locally Lipschitz continuous coefficients, and coefficients satisfy the contractive condition. The paper shows the existence and uniqueness of the solution of this equation. The author also studies the moment stability of the solution. The main result of the paper shows the existence and uniqueness of the invariant measure of the solution.