THE EXACT ASYMPTOTICS OF THE LARGE DEVIATION PROBABILITIES IN THE MULTIVARIATE BOUNDARY CROSSING PROBLEM
THE EXACT ASYMPTOTICS OF THE LARGE DEVIATION PROBABILITIES IN THE MULTIVARIATE BOUNDARY CROSSING PROBLEM
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DOI：
10.1017/apr.2019.28
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发表时间：
2019-09-01
影响因子：
1.2
通讯作者：
Borovkov, Konstantin A.
中科院分区：
文献类型：
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作者：
Pan, Yuqing;Borovkov, Konstantin A.
对于具有独立同分布跳跃且满足Cramer矩条件且平均向量至少有一个负分量的多元随机游动，我们得到了沿着固定的具有正分量的向量击中正向量的概率的精确渐近性.这个问题是由Avram等人的结果激发和推广的。(2008)关于二维风险过程的报告。我们的方法将Borovkov和Mogulskii在2000年左右发表的一系列论文中的大偏差技术与新的辅助结构相结合，使我们能够将他们关于具有光滑边界的命中远程集的结果推广到在“最可能的命中点”具有‘角’的边界的情况。我们还讨论了如何将我们的结果推广到更一般的目标集的情况。
For a multivariate random walk with independent and identically distributed jumps satisfying the Cramer moment condition and having mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being translated to infinity along a fixed vector with positive components. This problem is motivated by and extends results of Avram et al. (2008) on a two-dimensional risk process. Our approach combines the large deviation techniques from a series of papers by Borovkov and Mogulskii from around 2000 with new auxiliary constructions, enabling us to extend their results on hitting remote sets with smooth boundaries to the case of boundaries with a 'corner' at the 'most probable hitting point'. We also discuss how our results can be extended to the case of more general target sets.