The tail $\sigma$-fields of recurrent Markov processes

Isaac, Richard

doi:10.21136/AM.1977.103716

Geodesic

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The tail

σ

-fields of recurrent Markov processes

Isaac, Richard

Applications of Mathematics, Tome 22 (1977) no. 6, pp. 397-408.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

Let

{X_{n}, - \infty n + \infty}

be a Markov process with stationary transition probabilities having a

σ

-finite stationary measure and satisfying a weak recurrence condition. We investigate the structure of the forward and backward tail

σ

-fields,

\Cal T_{+ \infty}

and

\Cal T_{- \infty}

, under a variety of situations. The main result is a representation theorem for the sets of

\Cal T_{+ \infty}

; using this we develop a self-contained comprehensive treatment, deriving new as well as known theorems, including the decomposition into cyclically moving classes of processes satisfying the condition of Harris. The point of view and the techniques are probabilistic throughout.

MR Zbl

DOI : 10.21136/AM.1977.103716

Classification : 60B99, 60J05

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     author = {Isaac, Richard},
     title = {The tail $\sigma$-fields of recurrent {Markov} processes},
     journal = {Applications of Mathematics},
     pages = {397--408},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {1977},
     doi = {10.21136/AM.1977.103716},
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     zbl = {0375.60075},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1977.103716/}
}

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Isaac, Richard. The tail $\sigma$-fields of recurrent Markov processes. Applications of Mathematics, Tome 22 (1977) no. 6, pp. 397-408. doi : 10.21136/AM.1977.103716. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1977.103716/

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