Likelihood Ratio and Strong Limit Theorems for the Discrete Random Variable
Abstract: This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained. As a result, we obtain some strong deviation theorems for Poisson distribution and binomial distribution.
Cite this paper: W. Li, W. Wang and Z. Liu, "Likelihood Ratio and Strong Limit Theorems for the Discrete Random Variable," Open Journal of Discrete Mathematics, Vol. 2 No. 4, 2012, pp. 169-172. doi: 10.4236/ojdm.2012.24034.
References

[1]   W. Liu, “Relative Entropy Densities and a Class of Limit Theorems of Sequence of M-Valued Random Variables,” Annals of Probability, Vol. 18, No. 2, 1990, pp. 829-839. doi:10.1214/aop/1176990860

[2]   W. Liu, “Strong Deviation Theorems and Analytic Method,” Science Press, Beijing, 2003.

[3]   W. Liu, “A Kind of Strong Deviation Theorems for the Sequence of Nonnegative Integer-Valued Random Variables,” Statistics & Probability Letters, Vol. 32, No. 4, 1997, pp. 269-276.

[4]   W. Liu, “Some Limit Properties of the Multivariate Function Sequences of Discrete Random Variables,” Statistics & Probability Letters, Vol. 61, No. 1, 2003, pp. 41-50. doi:10.1016/S0167-7152(02)00304-8

[5]   W. G. Yang and X. Yang, “A Note on Strong Limit Theorems for Arbitrary Stochastic Sequences,” Statistics & Probability Letters, Vol. 78, No. 14, 2008, pp. 2018-2023. doi:10.1016/j.spl.2008.01.084

[6]   G. R. Li, S. Chen and J. H. Zhang, “A Class of Random Deviation Theorems and the Approach of Laplace Transform,” Statistics & Probability Letters, Vol. 79, No. 2, 2009, pp. 202-210. doi:10.1016/j.spl.2008.07.048

[7]   G. R. Li, S. Chen and S. Y. Feng, “A Strong Limit Theorem for Functions of Continuous Random Variables and an Extension of the Shannon-McMillan Theorem,” Journal of Applied Mathematics, Vol. 2008, 2008, pp. 1-10. doi:10.1155/2008/639145

[8]   W. G. Yang, “Some Limit Properties for Markov Chains Indexed by a Homogeneous Tree,” Statistics & Probability Letters, Vol. 65, No. 3, 2003, pp. 241-250. doi:10.1016/j.spl.2003.04.001

[9]   W. Liu, “Strong Deviation Theorems and Analytic Method (in Chinese) [M],” Science Press, Beijing, 2003.

[10]   J. L. Doob, “Stochastic Processes,” John Wiley & Sons, New York, 1953.

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