多维风险模型中独立和的局部大偏差

Local Precise Large Deviations for Independent Sums in Multi-Risk Model

中文关键词:  多维风险模型  O-正则变化函数  局部大偏差  正则密度.

英文关键词:multi-risk model  O-regularly varying function  local precise large deviations  regular density.

中文摘要:

      本文研究多维风险模型中独立和的问题. 假设存在$k$组随机变量.第$i(i=1,\ldots,k)$组记为$\{X_{ij},j\geq1\}$, 它们是i.i.d.的, 且均值有限. 密度函数记为$f_i(x)~(i=1,\ldots,k)$. 我们研究密度函数属于不同函数族时,$\sum_{i=1}^{k}S_{n_{i}}=\sum_{i=1}^{k}\sum_{j=1}^{n_{i}}X_{ij}$的局部大偏差. 得到了局部大偏差的定理并给予证明.

英文摘要:

      In this paper, we study the case of independent sums in multi-risk model. Assume that there exist $k$ types of variables. The $i$th are denoted by $\{X_{ij},j\geq1\}$, which are i.i.d. with common density function $f_i(x)\in\mathcal {OR}$ and finite mean, $i=1,\ldots,k$. We investigate local large deviations for partial sums $\sum_{i=1}^{k}S_{n_{i}}=\sum_{i=1}^{k}\sum_{j=1}^{n_{i}}X_{ij}$.