대한수학회논문집 (Communications of the Korean Mathematical Society)
- 제10권2호
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- Pages.409-417
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- 1995
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
GEOMETRIC ERGODICITY AND TRANSIENCE FOR NONLINEAR AUTOREGRESSIVE MONELS
초록
We consider the $R^k$-valued $(k \geq 1)$ process ${X_n}$ generated by $X_n + 1 = f(X_n)+e_{n+1}$, where $f(x) = (h(x),x^{(1)},x^{(1)},\cdots,x{(k-1)})'$. We assume that h is a real-valued measuable function on $R^k$ and that $e_n = (e'_n,0,\cdot,0)'$ where ${e'_n}$ are independent and identically distributed random variables. We obtained a practical criteria guaranteeing a given process to be geometrically ergodic. Sufficient condition for transience is also given.