Abstract
Criteria are derived for ergodicity and geometric ergodicity of Markov processes satisfyingX n+1 =f(X n )+σ(X n )ɛ n+1 , wheref, σ are measurable, {ɛ n } are i.i.d. with a (common) positive density,E|ɛ n |>∞. In the special casef(x)/x has limits, α, β asx→−∞ andx→+∞, 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.
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Bhattacharya, R.N., Lee, C. Ergodicity of nonlinear first order autoregressive models. J Theor Probab 8, 207–219 (1995). https://doi.org/10.1007/BF02213462
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DOI: https://doi.org/10.1007/BF02213462