Stochastic stability of monotone economies in regenerative environments

S. Foss, V. Schneer, Jonathan Thomas, Tim Worrall

Research output: Working paper

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 two canonical models in recursive economics, generalising 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 (1966) and Bhattacharya and Majumdar (2007).
Original languageEnglish
Number of pages34
Publication statusPublished - Jan 2015

Keywords

  • monotone economy
  • Markov Chain
  • stochastic recursion
  • driving sequences
  • regenerative sequences
  • existence and uniqueness of a stationary distribution
  • stochastic stability
  • Bewley-Huggett-Aiyagari Model
  • risk-sharing model
  • C61
  • C62

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