Ratio limit theorems for Markov chains
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- by J. F. C. Kingman and Steven Orey
- Proc. Amer. Math. Soc. 15 (1964), 907-910
- DOI: https://doi.org/10.1090/S0002-9939-1964-0173290-9
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References
- Kai Lai Chung, Markov chains with stationary transition probabilities, Die Grundlehren der mathematischen Wissenschaften, Band 104, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0116388
- K. L. Chung and P. Erdös, Probability limit theorems assuming only the first moment. I, Mem. Amer. Math. Soc. 6 (1951), 19. MR 40612 H. T. Croft, A question of limits, Eureka 20 (1957), 11-13.
- Adriano M. Garsia, Some Tauberian theorems and the asymptotic behavior of probabilities of recurrent events, J. Math. Anal. Appl. 7 (1963), 146–162. MR 157155, DOI 10.1016/0022-247X(63)90084-2
- J. F. C. Kingman, Ergodic properties of continuous-time Markov processes and their discrete skeletons, Proc. London Math. Soc. (3) 13 (1963), 593–604. MR 154334, DOI 10.1112/plms/s3-13.1.593
- Steven Orey, Strong ratio limit property, Bull. Amer. Math. Soc. 67 (1961), 571–574. MR 132600, DOI 10.1090/S0002-9904-1961-10694-0
- William E. Pruitt, Strong ratio limit property for $R$-recurrent Markov chains, Proc. Amer. Math. Soc. 16 (1965), 196–200. MR 174089, DOI 10.1090/S0002-9939-1965-0174089-0
Bibliographic Information
- © Copyright 1964 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 15 (1964), 907-910
- MSC: Primary 60.65
- DOI: https://doi.org/10.1090/S0002-9939-1964-0173290-9
- MathSciNet review: 0173290