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April, 1973 Strongly Ergodic Behavior for Non-Stationary Markov Processes
Richard W. Madsen, Dean L. Isaacson
Ann. Probab. 1(2): 329-335 (April, 1973). DOI: 10.1214/aop/1176996986


This paper considers ergodic behavior of those non-stationary Markov processes which can be represented by a sequence of stochastic kernels, $\{P_n(x, y)\}$, defined on a $\sigma$-finite measure space $(S, \mathscr{F}, \mu)$. In particular, the convergence of the superpositions, $P_1P_2P_3 \cdots P_n$, of these kernels is related to the convergence of their corresponding left eigenfunctions, $\psi_n$, where $\psi_n(y) = \int \psi_n(x)P_n(x, y)\mu(dx)$ and $\int \psi_n(y)\mu(dy) = 1$. It is then shown how these results can easily be extended to the general case where densities are not assumed.


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Richard W. Madsen. Dean L. Isaacson. "Strongly Ergodic Behavior for Non-Stationary Markov Processes." Ann. Probab. 1 (2) 329 - 335, April, 1973.


Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0264.60021
MathSciNet: MR350858
Digital Object Identifier: 10.1214/aop/1176996986

Primary: 60J05
Secondary: 60J10

Keywords: ergodic coefficient , left eigenfunctions , stochastic kernel , superposition , Weak and strong ergodicity

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 2 • April, 1973
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