| 关于任意随机变量序列泛函的强极限定理 |
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| 引用本文： | 邱德华,杨向群.关于任意随机变量序列泛函的强极限定理[J].数学杂志,2003,23(3):323-327. |
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| 作者姓名： | 邱德华 杨向群 |
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| 作者单位： | 1. 衡阳师范学院数学系,衡阳,421008
2. 湖南师范大学数学系,长沙,410081 |
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| 基金项目： | 国家自然科学基金(100710719)，湖南省教委科研基金 |
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| 摘 要： | 本文在k是固定的正整数，{fn}是R^k 1上的Borel可测函数列时，得到了任意随机变量序列{Xrn≥0}的泛函{fn(Xn-k,…,Xn)}的强极限定理，它是Chung的关于独立随机变量序列的强大数律的推广，作为推论，得到了k重非齐次马尔科夫链的一类强极限定理．
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| 关 键 词： | 强极限定理 鞅 k重非齐次马尔科夫链 |
| 文章编号： | 0255-7797(2003)03-0323-05 |
STRONG LIMIT THEOREMS ON FUNCTIONAL FOR THE SEQUENCE OF ARBITRARY RANDOM VARIABLES |
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| QIU De-hua.STRONG LIMIT THEOREMS ON FUNCTIONAL FOR THE SEQUENCE OF ARBITRARY RANDOM VARIABLES[J].Journal of Mathematics,2003,23(3):323-327. |
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| Authors: | QIU De-hua |
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| Abstract: | In this paper, we studies the strong limit theory of functional fn(xn-n),xn] for the sequence of arbitrary random variable Xn], where k is a positive integer, fn] is a sequence of Borel measurable functions on Rk+1, our results generalized Chang's strong law of large numbers for the sequence of independent random variables, as corollaries, a class of strong limit theorems for kth-order nonhomogeneous Markov Chain are obtained. |
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| Keywords: | strong limit theorem martingale kth-order nonhomogeneous Markov chain |
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