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Asymptotic properties of Markoff transition prababilities


Author: J. L. Doob
Journal: Trans. Amer. Math. Soc. 63 (1948), 393-421
MSC: Primary 60.0X
DOI: https://doi.org/10.1090/S0002-9947-1948-0025097-6
MathSciNet review: 0025097
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References [Enhancements On Off] (What's this?)

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  • [2] D. Blackwell, Idempotent Markoff chains, Ann. of Math. vol. 43 (1942) pp. 560-567. MR 0006632 (4:17b)
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  • [10] (Added in proof.) A. M. Yaglom, The ergodic principle for Markov processes with stationary distributions, C. R. (Doklady) Acad. Sci. URSS. N.S. vol. 54 (1947) pp. 347-349. The author supposes that $ {P^{(s)}}(x,A)$ is absolutely continuous with respect to a given self-reproducing distribution $ \Phi (A)$, with a positive continuous density, and proves that then $ {\lim _{s \to \infty }}{P^{(s)}}(x,A) = \Phi (A)$. This is a special case of Theorem 5.

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DOI: https://doi.org/10.1090/S0002-9947-1948-0025097-6
Article copyright: © Copyright 1948 American Mathematical Society

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