대한수학회지 (Journal of the Korean Mathematical Society)
- 제33권2호
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- Pages.227-234
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
SOME NECESSARY CONDITIONS FOR ERGODICITY OF NONLINEAR FIRST ORDER AUTOREGRESSIVE MODELS
초록
Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E