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| 1 | Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model显示文摘Consider a multidimensional renewal risk model, in which the claim sizes {X_k, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained. | SHEN Xin-mei FU Ke-ang ZHONG Xue-ting | 2018 | Applied Mathematics(A Journal of Chinese Universities)2018，33，4： | 1 |
| 2 | Precise Large Deviation for the Difference of Non-Random Sums of NA Random Variables显示文摘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. | Zhiqiang HUA Lixin SONG | 2016 | Journal of Mathematical Research with Applications2016，36，6： | 0 |
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