Ergodicity of nonlinear first order autoregressive models

Rabi N. Bhattacharya; Chanho Lee

doi:10.1007/BF02213462

Ergodicity of nonlinear first order autoregressive models

Rabi N. Bhattacharya, Chanho Lee

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

Criteria are derived for ergodicity and geometric ergodicity of Markov processes satisfying X_n+1 =f(X_n)+σ(X_n)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 language	English (US)
Pages (from-to)	207-219
Number of pages	13
Journal	Journal of Theoretical Probability
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/BF02213462
State	Published - Jan 1995
Externally published	Yes

Keywords

Autoregressive process
Brownian motion
Markov process
ergodicity

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1007/BF02213462

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abstract = "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.",

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author = "Bhattacharya, {Rabi N.} and Chanho Lee",

year = "1995",

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doi = "10.1007/BF02213462",

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T1 - Ergodicity of nonlinear first order autoregressive models

AU - Bhattacharya, Rabi N.

AU - Lee, Chanho

PY - 1995/1

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N2 - 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.

AB - 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.

KW - Autoregressive process

KW - Brownian motion

KW - Markov process

KW - ergodicity

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Ergodicity of nonlinear first order autoregressive models

Abstract

Keywords

ASJC Scopus subject areas

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