The existence of an invariant probability measure is proven for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster expansion method, from Gibbs field theory. It holds for small perturbations of ergodic diffusions.
"Exponential ergodicity for a class of non-Markovian stochastic processes." Braz. J. Probab. Stat. 34 (3) 658 - 684, August 2020. https://doi.org/10.1214/19-BJPS440