基于Bernstein Copula函数的随机变量序列的Max-Sum局部等价式

Local Max-sum Equivalence of Random Variables with Bernstein Copula

该文考虑一类具有局部长尾分布,但不一定具有相同分布的随机变量序列,其联合分布由Bernstein copula函数进行联系.研究其部分和及其最大值的局部分布的渐近性质.在假设诸随机变量服从局部次指数分布的条件下,得到了Max-Sum局部等价性.该等价性从局部和相依的角度描述了随机游动的一次大跳原理.数值实验表明所得结果稳定可行.

In this paper,we consider a sequence of non-negative dependent and not necessarily identically distributed random variables with local long-tailed marginal distributions and Bernstein copula and study the local asymptotic behavior of the tail of their partial sum and maximum.Then,under a suitable condition for local subexponentiality,we obtain the local max-sum equivalence.The result indicates that the big-jump principle of random walks remains valid in its local version under more general dependency assumptions.The numerical experimental results under different parameter settings further validate the stability and feasibility of the obtained results.