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July, 1988 Asymptotics of a Class of Markov Processes Which Are Not in General Irreducible
Rabi N. Bhattacharya, Oesook Lee
Ann. Probab. 16(3): 1333-1347 (July, 1988). DOI: 10.1214/aop/1176991694


Let $\mathbf{\alpha}_n$ be a sequence of i.i.d. nondecreasing random maps on a subset $S$ of $\mathbb{R}^k$ into itself and let $X_0$ be a random variable with values in $S$ independent of the sequence $\mathbf{\alpha}_n$. Then $X_n \equiv \mathbf{\alpha}_n \cdots \mathbf{\alpha}_1X_0$ is a Markov process. Conditions for the existence of unique invariant probabilities are obtained for such Markov processes which are not in general irreducible, extending earlier results of Dubins and Freedman to multidimensional and noncompact state spaces. In addition, a functional central limit theorem is obtained. These yield new results in time series and economic models.


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Rabi N. Bhattacharya. Oesook Lee. "Asymptotics of a Class of Markov Processes Which Are Not in General Irreducible." Ann. Probab. 16 (3) 1333 - 1347, July, 1988.


Published: July, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0652.60028
MathSciNet: MR942772
Digital Object Identifier: 10.1214/aop/1176991694

Primary: 60F05
Secondary: 60J05

Keywords: central limit theorems , Fixed points , invariant probability , nondecreasing maps

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 3 • July, 1988
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