A new theorem on the existence of invariant distributions with applications to ARCH processes

被引：11

作者：

Kazakevicius, V

Leipus, R

机构：

[1] Vilnius State Univ, Dept Math & Informat, LT-2600 Vilnius, Lithuania

[2] Vilnius State Univ, Inst Math & Informat, LT-2600 Vilnius, Lithuania

来源：

JOURNAL OF APPLIED PROBABILITY | 2003年 / 40卷 / 01期

关键词：

Markov chain; invariant distribution; integrated ARCH process; nonlinear time series;

D O I：

10.1017/S0021900200022312

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A new theorem on the existence of an invariant initial distribution for a Markov chain evolving on a Polish space is proved. As an application of the theorem, sufficient conditions for the existence of integrated ARCH processes are established. In the case where these conditions are violated, the top Lyapunov exponent is shown to be zero.

引用

页码：147 / 162

页数：16

共 22 条

[1]

[Anonymous], 1965, FUNCTIONAL ANAL

[2] Fractionally integrated generalized autoregressive conditional heteroskedasticity [J].