Ergodicity of nonlinear first order autoregressive models

Rabi N. Bhattacharya, Chanho Lee

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


Criteria are derived for ergodicity and geometric ergodicity of Markov processes satisfying Xn+1 =f(Xn)+σ(Xn)e{open}n+1, where f, σ are measurable, {e{open}n} are i.i.d. with a (common) positive density, E|e{open}n|>∞. In the special case f(x)/x has limits, α, β as x→-∞ and x→+∞, respectively, it is shown that "α<1, β<1, αβ<1" is sufficient for geometric ergodicity, and that "α<-1, β≤1, αβ≤1" is necessary for recurrence.

Original languageEnglish (US)
Pages (from-to)207-219
Number of pages13
JournalJournal of Theoretical Probability
Issue number1
StatePublished - Jan 1995
Externally publishedYes


  • Autoregressive process
  • Brownian motion
  • Markov process
  • ergodicity

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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