Stochastic Stability of Monotone Economies in Regenerative Environments

TL;DR

This paper introduces a new class of monotone stochastic recursions in regenerative environments, extending stability analysis beyond Markov chains to more general dependent sequences in economic models.

Contribution

It generalizes stability results for monotone stochastic recursions to regenerative environments, broadening applicability beyond traditional Markov chain assumptions.

Findings

Proves stability theorems for the new class of recursions.

Applies results to three canonical models in recursive economics.

Generalizes known stability results to dependent, non-i.i.d. sequences.

Abstract

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.