| 负相协随机变量非随机和的差的精确大偏差 |
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| 引用本文： | 华志强,宋立新.负相协随机变量非随机和的差的精确大偏差[J].数学研究及应用,2016,36(6):732-740. |
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| 作者姓名： | 华志强 宋立新 |
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| 作者单位： | 内蒙古民族大学数学学院, 内蒙古 通辽 028043,大连理工大学数学科学学院, 辽宁 大连 116024 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11371077; 11571058), 中央高校基本科研业务费专项基金(Grant No.DUT15LK19),内蒙古民族大学自然科学基金(Grant Nos.NMDYB1436; NMDYB1437). |
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| 摘 要： | In this paper,we study precise large deviation for the non-random difference sum from j=1 to n_1(t) X_(1j)-sum from j=1 to n_2(t) X_(2j),where sum from j=1 to n_1(t) X_(1j) is the non-random sum of {X_(1j),j≥1} which is a sequence of negatively associated random variables with common distribution F_1(x),and sum from j=1 to n_2(t) X_(2j) is the non-random sum of {X_(2j),j≥1} which is a sequence of independent and identically distributed random variables,n_1(t) and n_2(t) are two positive integer functions.Under some other mild conditions,we establish the following uniformly asymptotic relation lim t→∞ sup x≥r(n_1(t))~(p+1)|(P(∑~(n_1(t)_(j=1)X_(1j)-∑~(n_2(t)_(j=1)X_(2j)-(μ_1n_1(t)-μ_2n_2(t)x))/(n_1(t)F_1(x))-1|=0.
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| 关 键 词： | 精确大偏差 负相协 一致变化尾 差 |
| 收稿时间： | 2015/8/21 0:00:00 |
| 修稿时间： | 2015/12/1 0:00:00 |
Precise Large Deviation for the Difference of Non-Random Sums of NA Random Variables |
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| Zhiqiang HUA and Lixin SONG.Precise Large Deviation for the Difference of Non-Random Sums of NA Random Variables[J].Journal of Mathematical Research with Applications,2016,36(6):732-740. |
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| Authors: | Zhiqiang HUA and Lixin SONG |
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| Institution: | College of Mathematics, Inner Mongolia University for the Nationalities, Inner Mongolia 028043, P. R. China and School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | In this paper, we study precise large deviation for the non-random difference $\sum_{j=1}^{n_1(t)}X_{1j}$ $-\sum_{j=1}^{n_2(t)}X_{2j}$, where $\sum_{j=1}^{n_1(t)}X_{1j}$ is the non-random sum of $\{X_{1j},j\geq 1\}$ which is a sequence of negatively associated random variables with common distribution $F_{1}(x)$, and $\sum_{j=1}^{n_2(t)}X_{2j}$ is the non-random sum of $\{X_{2j},j\geq 1\}$ which is a sequence of independent and identically distributed random variables, $n_1(t)$ and $n_2(t)$ are two positive integer functions. Under some other mild conditions, we establish the following uniformly asymptotic relation $$\lim_{t\rightarrow\infty}\sup_{x\geq\gamma (n_{1}(t))^{p+1}}\Big|\frac{P(\sum_{j=1}^{n_1(t)}X_{1j}-\sum_{j=1}^{n_2(t)}X_{2j}-(\mu_{1}n_{1}(t)-\mu_{2}n_{2}(t))>x)}{n_{1}(t)\bar{F_{1}}(x)}-1\Big|=0.$$ |
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| Keywords: | precise large deviation negative association consistently varying tail difference |
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