# Journal of Advanced Statistics

### On Some Limit Properties for (an, (n))-Asymptotic Circular Markov Chains

Download PDF (549.1 KB) PP. 31 - 43 Pub. Date: September 1, 2018

### Author(s)

**Dabin Zhang**^{*}

School of Mathematics and Physics, AnHui University of Technology, Ma’anshan, 243002, China**Yun Dong**

School of Mathematics, Maanshan Teachers’ College, Maanshan, 243041, China

### Abstract

### Keywords

### References

[1] P. H. Algoet and T. M. Cover, “A sandwich proof of the shannon-mcmillan-breiman theorem,” Annals of Probability, vol. 16, no. 2, pp. 899–909, 1988.

[2] A. R. Barron, “The strong ergodic theorem for densities: Generalized shannon-mcmillan-breiman theorem,” Annals of Probability, vol. 13, no. 4, pp. 1292–1303, 1985.

[3] J. C. Kieffer, “A simple proof of the moy-perez generalization of the shannon-mcmillan theorem.” Pacific Journal of Mathematics, vol. 51, no. 1, pp. 203–206, 1974.

[4] C. A. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, no. 4, pp. 379–423, 1948.

[5] B. Bowerman, H. T. David, and D. Isaacson, “The convergence of cesaro averages for certain nonstationary markov chains,” Stochastic Processes & Their Applications, vol. 5, no. 3, pp. 221–230, 1977.

[6] T. S. Chiang and Y. Chow, “A limit theorem for a class of inhomogeneous markov processes,” Annals of Probability, vol. 17, no. 4, pp. 1483–1502, 1989.

[7] J. B. T. M. Roerdink and K. E. Shuler, “Asymptotic properties of multistate random walks. i. theory,” Journal of Statistical Physics, vol. 40, no. 1-2, pp. 205–240, 1985.

[8] W. Yang, B. Wang, and Z. Shi, “Strong law of large numbers for countable asymptotic circular markov chains,” Journal of Jiangsu University, vol. 43, no. 18, pp. 3943–3954, 2011.

[9] P. Zhong, W. Yang, and P. Liang, “The asymptotic equipartition property for asymptotic circular markov chains,” Probability in the Engineering and Informational Sciences, vol. 24, no. 2, pp. 279–288, 2010.

[10] Z. Wang and W. Yang, “The generalized entropy ergodic theorem for nonhomogeneous markov chains,” Journal of Theoretical Probability, vol. 29, no. 3, pp. 761–775, 2016.

[11] K. L. Chung, “A note on the ergodic theorem of information theory,” Annals of Mathematical Statistics, vol. 32, no. 2, pp. 612–614, 1961.