Stability in distribution of neutral stochastic functional differential equations

In this note, by the weak convergence approach, we investigate stability in distribution for a range of neutral stochastic functional differential equations. As a byproduct, our result derived also implies existence of invariant measure of the semigroup generated by the segment process. Last but not least, we close some gaps of Lemma 2, and improve greatly Lemma 4 due to Hu and Wang (2012).