Invariant Measures for Stochastic Differential Equations

Abstract

For ergodic SDEs, when solving them numerically, it is extremely important to choose proper schemes which could possess the properties under consideration and be applicable to practice. To the best of our knowledge, the numerical analysis of ergodic SDEs usually follows two directions. One is to construct numerical schemes which could inherit the ergodicity of the original system, and then to give the approximate error between the numerical invariant measure and the original one.