# SOME NECESSARY CONDITIONS FOR ERGODICITY OF NONLINEAR FIRST ORDER AUTOREGRESSIVE MODELS

• Lee, Chan-Ho
• Published : 1996.05.01
• 35 3

#### Abstract

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, $E$\mid$\epsilon_n$\mid$< \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

#### Keywords

Markov process;ergodicity;invariant probability