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Correction to: Random Coefficient Autoregressive Processes: a Markov Chain Analysis of Stationarity and Finiteness of Moments by Paul D. Feigin and Richard L. Tweedie J. Time Series Anal., Vol. 6, No. 1 (1985)
Journal of Time Series Analysis ( IF 0.9 ) Pub Date : 2020-03-16 , DOI: 10.1111/jtsa.12521 Paul D. Feigin 1
中文翻译:
校正至:随机系数自回归过程:平稳性和矩有限度的马尔可夫链分析,作者:Paul D. Feigin和Richard L. Tweedie J.时间序列分析,第一卷。6,No.1(1985)
更新日期:2020-03-16
Journal of Time Series Analysis ( IF 0.9 ) Pub Date : 2020-03-16 , DOI: 10.1111/jtsa.12521 Paul D. Feigin 1
Affiliation
The statement of Theorem 1 in Feigin and Tweedie (1985) is incomplete if it is to be a consequence of Theorem 4(ii) in Tweedie (1983a). Theorem 1 should read as below with (2.1a) and aperiodicity being the extra conditions. Indeed, we provide a counterexample to the original formulation.
Theorem 1.Suppose that {Xt} is an aperiodic Feller chain, that there exists a measure φ and a compact set A with φ(A)>0 such that
- (i)
{Xt} is φ‐irreducible
- (ii)
there exists a non‐negative continuous function satisfying
(2.1)(2.1a)
and for some δ>0
(2.2)
Then {Xt} is geometrically ergodic.
中文翻译:
校正至:随机系数自回归过程:平稳性和矩有限度的马尔可夫链分析,作者:Paul D. Feigin和Richard L. Tweedie J.时间序列分析,第一卷。6,No.1(1985)
如果是Tweedie(1983a)中定理4(ii)的结果,则Feigin和Tweedie(1985)中的定理1的陈述是不完整的。定理1应读为(2.1a),且非周期性为附加条件。确实,我们提供了原始公式的反例。
定理1.假设{ X t }是一个非周期Feller链,存在一个测度φ和一个紧集A,且φ(A)> 0使得
- (一世)
{ X t }是φ-不可约的
- (ii)
存在一个非负连续函数 满意的
(2.1)(2.1a)
并且对于δ > 0
(2.2)
那么{ X t }是几何遍历的。