We introduce and analyze a new class of monotone stochastic recursions in a regenerative environment which is essentially broader than that of Markov chains. We prove stability theorems and apply our results to three canonical models in recursive economics, generalizing some known stability results to the cases when driving sequences are not independent and identically distributed.
Foss, S., Shneer, V., Thomas, J. P., & Worrall, T. (2018). Stochastic stability of monotone economies in regenerative environments. Journal of Economic Theory, 173, 334–360. https://doi.org/10.1016/j.jet.2017.11.004