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Stochastic Stability of Monotone Economies in Regenerative Environments

Stochastic Stability of Monotone Economies in Regenerative Environments

by Jonathan Thomas, Tim Worrall, Sergey Foss and Vsevolod Shneer

Abstract

We introduce and analyse 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. We also revisit the case of monotone Markovian models (or, equivalently, stochastic recursions with i.i.d. drivers) and provide a simplified version of the proof of a stability result given previously by Dubins and Freedman and Bhattacharya and Majumdar.

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