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