应用Fuk Nagaev不等式求相依随机场的全收敛定理
An approach to complete convergence theorems for dependent random fields via application of Fuk Nagaev inequality
摘要：
令$\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}$为随机域，即由$\mathbb{N}^d $、$d\ge 2$索引的随机变量族。利用N-Nagaev不等式研究了非同分布、负相依和鞅随机场随机场的全收敛、收敛速度.在赋范序列为$n_1^{α_1}\cdot n_2^{α_2}\cdot\ldots\cdot n_d^{α_d}$的情况下证明了这些结果的非对称收敛性，其中$(n_1,n_2,\ldots, n_d)=\mathbf{n} \in \mathbb{N}^d$和$\min\limits_{1\leq i \leq d}α_i \geq \frac{1}{2}.$
英文摘要：
Let $\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}$ be a random field i.e. a family of random variables indexed by $\mathbb{N}^d $, $d\ge 2$. Complete convergence, convergence rates for non identically distributed, negatively dependent and martingale random fields are studied by application of Fuk-Nagaev inequality. The results are proved in asymmetric convergence case i.e. for the norming sequence equal $n_1^{α_1}\cdot n_2^{α_2}\cdot\ldots\cdot n_d^{α_d}$, where $(n_1,n_2,\ldots, n_d)=\mathbf{n} \in \mathbb{N}^d$ and $\min\limits_{1\leq i \leq d}α_i \geq \frac{1}{2}.$
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
