# 关于整值随机序列滑动平均的若干小偏差定理On Small Deviation Theorems for Moving Averages of Dependent Integer-Valued Random Sequence

Abstract:
In this paper, the notion of moving likelihood ratio, as a measure of the deviation of a sequence of integer-valued random variables from an independent random sequence with geometric distribution, is intro-duced. By restricting the moving likelihood ratio, a certain subset of the sample space is given, and on this subset, a class of strong laws, represented by inequalities, are obtained. These strong laws contain some limit properties of the sequence of integer-valued random variables, concerning relative entropy density and the entropy function of geometric distribution.

[1] T. L. Lai. Summability methods for independent identically distributed random varibles. Proceeding of American Mathematical Society, 1974, 45(2): 253-261.

[2] N. C. Jain. Tail probabilities for sums of independent Banach space valued random variables. Probability Theory and Related Fields, 1975, 33(3): 155-166.

[3] V. F. Gaposhkin. The law of large numbers for movingaverages of independent random. Mathematicheskie Zametki, 1987, 42(1): 124-131.

[4] 刘文. 强偏差定理与分析方法[M]. 北京: 科学出版社, 2002.

[5] P. Barron. The strong ergodic theorem for densitics: Generalized Shannon-McMillan-Breiman theorem. The Annals of Probability, 1985, 13(4): 1292-1303.

[6] M. Loeve. Probability Theory I. New York: Springer, 1977.

Top