Existence of stationary distributions for a class of nonlinear time series models in random environment domain
oleh: Xu Yong, Wang Yueheng, Zhu Enwen
| Format: | Article |
|---|---|
| Diterbitkan: | SpringerOpen 2011-01-01 |
Deskripsi
<p>Abstract</p> <p>In this paper, we study the problem of a variety of nonlinear time series model <it>X</it><sub><it>n</it>+1 </sub>= <it>F</it>(<it>X<sub>n</sub></it>, <it>e</it><sub><it>n</it>+1</sub>(<it>Z</it><sub><it>n</it>+1</sub>)) in which {<it>Z</it><sub><it>n</it>+1</sub>} is a Markov chain with finite state space, and for every state <it>i </it>of the Markov chain, {<it>e<sub>n</sub></it>(<it>i</it>)} is a sequence of independent and identically distributed random variables. Also, the existence of the stationary distribution of the sequence {<it>X<sub>n</sub></it>} defined by the above model is investigated. Some new novel results on the underlying models are presented.</p> <p><b>2010 Mathematics Subject Classification</b>: 60J10</p>