Invariant Measures for Path-Dependent Random Diffusions - Chenggui Yuan (ArXiv: 1706.05638)
In this paper, we investigate the existence and uniqueness of invariant measure of stochastic functional differential equations with Markovian switching. Under an average condition, we prove that there is a unique measure for the exact solutions and the corresponding Euler numerical solutions. Moreover, the invariant measure of the Euler numerical solutions will converge to that of the exact solutions as the step size tends to zero.