We establish new general sufficient conditions for the existence of an invariant measure for stochastic functional differential equations and exponential or subexponential convergence to the equilibrium. The obtained conditions extend the Veretennikov–Khasminskii conditions for SDEs and are optimal in a certain sense.
"Invariant measures for stochastic functional differential equations." Electron. J. Probab. 22 1 - 23, 2017. https://doi.org/10.1214/17-EJP122